Geometric group theory:
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| Language: | English |
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Providence, Rhode Island
American Mathematical Society
[2018]
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| Series: | American Mathematical Society: Colloquium publications
Volume 63 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xx, 819 Seiten Illustrationen, Diagramme |
| ISBN: | 9781470411046 1470411040 |
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| 100 | 1 | |a Druţu, Cornelia |d 1967- |0 (DE-588)1035530821 |4 aut | |
| 245 | 1 | 0 | |a Geometric group theory |c Cornelia Druţu ; Michael Kapovich ; with an appendix by Bogdan Nica |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2018] | |
| 264 | 4 | |c © 2018 | |
| 300 | |a xx, 819 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a American Mathematical Society: Colloquium publications |v Volume 63 | |
| 650 | 0 | 7 | |a Geometrische Gruppentheorie |0 (DE-588)4651615-3 |2 gnd |9 rswk-swf |
| 653 | 0 | |a Geometric group theory | |
| 653 | 0 | |a Group theory | |
| 653 | 0 | |a Geometric group theory | |
| 653 | 0 | |a Group theory | |
| 653 | 0 | |a Group theory and generalizations / Special aspects of infinite or finite groups / Geometric group theory | |
| 653 | 0 | |a Group theory and generalizations / Special aspects of infinite or finite groups / Hyperbolic groups and nonpositively curved groups | |
| 653 | 0 | |a Group theory and generalizations / Special aspects of infinite or finite groups / Asymptotic properties of groups | |
| 653 | 0 | |a Group theory and generalizations / Special aspects of infinite or finite groups / Generators, relations, and presentations | |
| 653 | 0 | |a Group theory and generalizations / Special aspects of infinite or finite groups / Solvable groups, supersolvable groups | |
| 653 | 0 | |a Group theory and generalizations / Special aspects of infinite or finite groups / Nilpotent groups | |
| 653 | 0 | |a Group theory and generalizations / Special aspects of infinite or finite groups / Fundamental groups and their automorphisms | |
| 653 | 0 | |a Group theory and generalizations / Structure and classification of infinite or finite groups / Groups acting on trees | |
| 653 | 0 | |a Group theory and generalizations / Structure and classification of infinite or finite groups / Residual properties and generalizations; residually finite groups | |
| 653 | 0 | |a Manifolds and cell complexes / Low-dimensional topology / Topological methods in group theory | |
| 689 | 0 | 0 | |a Geometrische Gruppentheorie |0 (DE-588)4651615-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Kapovich, Michael |d 1963- |0 (DE-588)134100409 |4 aut | |
| 700 | 1 | |a Nica, Bogdan |d 1977- |0 (DE-588)1156786754 |4 ctb | |
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Record in the Search Index
| _version_ | 1817069496138989568 |
|---|---|
| adam_text |
Contents
Preface xiii
Chapter 1. Geometry and topology 1
1.1. Set-theoretic preliminaries 1
1.1.1. General notation 1
1.1.2. Growth rates of functions 2
1.1.3. Jensen’s inequality 3
1.2. Measure and integral 3
1.2.1. Measures 3
1.2.2. Finitely additive integrals 5
1.3. Topological spaces. Lebesgue covering dimension 7
1.4. Exhaustions of locally compact spaces 10
1.5. Direct and inverse limits 11
1.6. Graphs 13
1.7. Comx lexes and homology 17
1.7.1. Simplicial complexes 17
1.7.2. Cell complexes 19
Chapter 2. Metric spaces 23
2.1. General metric spaces 23
2.2. Length metric spaces 25
2.3. Graphs as length spaces 27
2.4. Hausdorff and Gromov-Hausdorff distances. Nets 28
2.5. Lipschitz maps and Banach---Mazur distance 30
2.5.1. Lipschitz and locally Lipschitz maps 30
2.5.2. Bi-Lipschitz maps. The Banach-Mazur distance 33
2.6. Hausdorff dimension 34
2.7. Norms and valuations 35
2.8. Norms on field extensions. Adeles 39
2.9. Metrics on affine and projective spaces 43
2.10. Quasiprojective transformations. Proximal transformations 48
2.11. Kernels and distance functions 51
Chapter 3. Differential geometry 59
3.1. Smooth manifolds 59
3.2. Smooth partition of unity 61
3.3. Riemannian metrics 61
3.4. Riemannian volume 64
3.5. Volume growth and isoperimetric functions. Cheeger constant 68
3.6. Curvature 71
v
vi CONTENTS
3.7. Riernannian manifolds of bounded geometry 73
3.8. Metric simplicial complexes of bounded geometry and systolic
inequalities 74
3.9. Harmonic functions 79
3.10. Spectral interpretation of the Cheeger constant 82
3.11. Comparison geometry 82
3.11.1. Alexandrov curvature and CAT(k) spaces 82
3.11.2. Cartan’s Fixed-Point Theorem 86
3.11.3. Ideal boundary, horoballs and horospheres 88
Chapter 4. Hyperbolic space 91
4.1. Moebius transformations 91
4.2. Real-hyperbolic space 94
4.3. Classification of isometries 99
4.4. Hyperbolic trigonometry 102
4.5. Triangles and curvature of HP 105
4.6. Distance function on HP 108
4.7. Hyperbolic balls and spheres 110
4.8. Horoballs and horospheres in HP 110
4.9. HP as a symmetric space 112
4.10. Inscribed radius and thinness of hyperbolic triangles 116
4.11. Existence-uniqueness theorem for triangles 118
Chapter 5. Groups and their actions 119
5.1. Subgroups 120
5.2. Virtual isomorphisms of groups and commensurators 122
5.3. Commutators and the commutator subgroup 124
5.4. Semidirect products and short exact sequences 126
5.5. Direct sums and wreath products 128
5.6. Geometry of group actions 129
5.6.1. Group actions 129
5.6.2. Linear actions 133
5.6.3. Lie groups 134
5.6.4. Haar measure and lattices 137
5.6.5. Geometric actions 140
5.7. Zariski topology and algebraic groups 140
5.8. Group actions on complexes 147
5.8.1. G-complexes 147
5.8.2. Borel and Haefliger constructions 148
5.8.3. Groups of finite type 159
5.9. Cohomology 160
5.9.1. Group rings and modules 160
5.9.2. Group cohomology 161
5.9.3. Bounded cohomology of groups 165
5.9.4. Ring derivations 166
5.9.5. Derivations and split extensions 168
5.9.6. Central coextensions and second cohomology 171
CONTENTS
Chapter 6. Median spaces and spaces with measured walls
6.1. Median spaces
6.1.1. A review of median algebras
6.1.2. Convexity
6.1.3. Examples of median metric spaces
6.1.4. Convexity and gate property in median spaces
6.1.5. Rectangles and parallel pairs
6.1.6. Approximate geodesics and medians; completions of median
spaces
6.2. Spaces with measured walls
6.2.1. Definition and basic properties
6.2.2. Relationship between median spaces and spaces
with measured walls
6.2.3. Embedding a space with measured walls in a median space
6.2.4. Median spaces have measured walls
Chapter 7. Finitely generated and finitely presented groups
7.1. Finitely generated groups
7.2. Free groups
7.3. Presentations of groups
7.4. The rank of a free group determines the group. Subgroups
7.5. Free constructions: Amalgams of groups and graphs of groups
7.5.1. Amalgams
7.5.2. Graphs of groups
7.5.3. Converting graphs of groups into amalgams
7.5.4. Topological interpretation of graphs of groups
7.5.5. Constructing finite index subgroups
7.5.6. Graphs of groups and group actions on trees
7.6. Ping-pong lemma. Examples of free groups
7.7. Free subgroups in SU(2)
7.8. Ping-pong on projective spaces
7.9. Cayley graphs
7.10. Volumes of maps of cell complexes and Van Kampen diagrams
7.10.1. Simplicial, cellular and combinatorial volumes of maps
7.10.2. Topological interpretation of finite-presentability
7.10.3. Presentations of central coextensions
7.10.4. Dehn function and van Kampen diagrams
7.11. Residual finiteness
7.12. Hopfian and co-hopfian properties
7.13. Algorithmic problems in the combinatorial group theory
Chapter 8. Coarse geometry
8.1. Quasiisometry
8.2. Group-theoretic examples of quasiisometries
8.3. A metric version of the Milnor- Schwarz Theorem
8.4. Topological coupling
8.5. Quasi act ions
8.6. Quasiisometric rigidity problems
8.7. The growth function
175
175
176
177
178
180
182
185
186
186
189
190
192
199
199
203
206
212
213
213
214
216
216
217
219
222
226
226
227
235
235
236
236
238
244
247
248
251
251
261
267
269
271
274
275
CONTENTS
viii
8.8. Codimension one isoperimetrie inequalities 281
8.9. Distortion of a subgroup in a group 283
Chapter 9. Coarse topology 287
9.1. Ends 287
9.1.1. The number of ends 287
9.1.2. The space of ends 290
9.1.3. Ends of groups 295
9.2. Rips complexes and coarse homotopy theory 297
9.2.1. Rips complexes 297
9.2.2. Direct system of Rips complexes and coarse homotopy 299
9.3. Metric cell complexes 300
9.4. Connectivity and coarse connectivity 306
9.5. Retractions 312
9.6. Poincare duality and coarse separation 314
9.7. Metric filling functions 317
9.7.1. Coarse isoperimetrie functions and coarse filling radius 318
9.7.2. Quasiisometric invariance of coarse filling functions 320
9.7.3. Higher Dehn functions 325
9.7.4. Coarse Besikovitch inequality 330
Chapter 10. Ultralimits of metric spaces 333
10.1. The Axiom of Choice and its weaker versions 333
10.2. Ultrafilters and the Stone-Cech compactification 339
10.3. Elements of non-standard algebra 340
10.4. Ultralimits of families of metric spaces 344
10.5. Completeness of ultralimits and incompleteness of ultrafilters 348
10.6. Asymptotic cones of metric spaces 352
10.7. Ultralimits of asymptotic cones are asymptotic cones 356
10.8. Asymptotic cones and quasiisometries 358
10.9. Assouad-type theorems 360
Chapter 11. Gromov-hyperbolic spaces and groups 363
11.1. Hyperbolicity according to Rips 363
11.2. Geometry and topology of real trees 367
11.3. Gromov hyperbolicity 368
11.4. Ultralimits and stability of geodesics in Rips-hyperbolic spaces 372
11.5. Local geodesics in hyperbolic spaces 376
11.6. Quasiconvexity in hyperbolic spaces 379
11.7. Nearest-point projections 381
11.8. Geometry of triangles in Rips-hyperbolic spaces 382
11.9. Divergence of geodesics in hyperbolic metric spaces 385
11.10. Morse Lemma revisited 387
11.11. Ideal boundaries 390
11.12. Gromov bordification of Gromov-hyperbolic spaces 398
11.13. Boundary extension of quasiisometries of hyperbolic spaces 402
11.13.1. Extended Morse Lemma 402
11.13.2. The extension theorem 404
11.13.3. Boundary extension and quasiactions 406
CONTENTS
IX
11.13.4, Conical limit points of quasiactions 407
11.14. Hyperbolic groups 407
11.15. Ideal boundaries of hyperbolic groups . 410
11.16. Linear isoperimetric inequality and Dehn algorithm
for hyperbolic groups 414
11.17. The small cancellation theory 417
11.18. The Rips construction 418
11.19. Central coextensions of hyperbolic groups and quasi isometries 419
11.20. Characterization of hyperbolicity using asymptotic cones 423
11.21. Size of loops 429
11.21.1. The minsize 429
11.21.2. The constriction 430
11.22. Filling invariants of hyperbolic spaces 432
11.22.1. Filling area 433
11.22.2. Filling radius 434
11.22.3. Orders of Dehn functions of non-hyperbolic groups and higher
Dehn functions 437
11.23. Asymptotic cones, actions on trees and isometric actions
on hyperbolic spaces 438
11.24. Summary of equivalent definitions of hyperbolicity 441
11.25. Further properties of hyperbolic groups 442
11.26. Relatively hyperbolic spaces and groups 445
Chapter 12. Lattices in Lie groups 449
12.1. Semisirnple Lie groups and their symmetric spaces 449
12.2. Lattices 451
12.3. Examples of lattices 452
12.4. Rigidity and superrigidity 454
12.5. Commensurators of lattices 456
12.6. Lattices in PO(n, 1) 456
12.6.1. Zariski density 456
12.6.2. Parabolic elements and non-compactness 458
12.6.3. Thick-thin decomposition 460
12.7. Central coextensions 462
Chapter 13. Solvable groups 465
13.1. Free abelian groups 465
13.2. Classification of finitely generated abelian groups 468
13.3. Automorphisms of Zn 471
13.4. Nilpotent groups 474
13.5. Polycyclic groups 484
13.6. Solvable groups: Definition and basic properties 489
13.7. Free solvable groups and the Magnus embedding 491
13.8. Solvable versus polycyclic 493
Chapter 14. Geometric aspects of solvable groups 497
14.1. Wolf’s Theorem for semidirect products Zn x Z 497
14.1.1. Geometry of Hs (Z) 499
14.1.2. Distortion of subgroups of solvable groups 503
X
CONTENTS
14.1.3. Distortion of subgroups in nilpotent groups 505
14.2. Polynomial growth of nilpotent groups 514
14.3. Wolf’s Theorem 515
14.4. Milnor’s Theorem 517
14.5. Failure of QI rigidity for solvable groups 520
14.6. Virtually nilpotent subgroups of GL(n) 521
14.7. Discreteness and nilpotence in Lie groups 524
14.7.1. Some useful linear algebra 524
14.7.2. Zassenhaus neighborhoods 525
14.7.3. Jordan’s Theorem 528
14.8. Virtually solvable subgroups of GL(n, C) 530
Chapter 15. The Tits Alternative 537
15.1. Outline of the proof 538
15.2. Separating sets 540
15.3. Proof of the existence of free subsemigroups 541
15.4. Existence of very proximal elements: Proof of Theorem 15.6 541
15.4.1. Proximality criteria 542
15.4.2. Constructing very proximal elements 543
15.5. Finding ping-pong partners: Proof of Theorem 15.7 545
15.6. The Tits Alternative without finite generation assumption 546
15.7. Groups satisfying the Tits Alternative 547
Chapter 16. Gromov’s Theorem 549
16.1. Topological transformation groups 549
16.2. Regular Growth Theorem 551
16.3. Consequences of the Regular Growth Theorem 555
16.4. Weakly polynomial growth 556
16.5. Displacement function 557
16.6. Proof of Gromov’s Theorem 558
16.7. Quasiisometric rigidity of nilpotent and abelian groups 561
16.8. Further developments 562
Chapter 17. The Banach-Tarski Paradox 565
17.1. Paradoxical decompositions 565
17.2. Step 1: A paradoxical decomposition of the free group 568
17.3. Step 2: The Hausdorff Paradox 569
17.4. Step 3: Spheres of dimension ^ 2 are paradoxical 570
17.5. Step 4: Euclidean unit balls are paradoxical 571
Chapter 18. Amenability and paradoxical decomposition 573
18.1. Amenable graphs 573
18.2. Amenability and quasiisometry 578
18.3. Amenability of groups 583
18.4. Fplner Property 588
18.5. Amenability, paradoxality and the F0lner Property 592
18.6. Supramenability and weakly paradoxical actions 596
18.7. Quantitative approaches to non-amenability and
weak paradoxality 601
18.8. Uniform amenability and ultrapowers 606
CONTENTS xi
18.9. Quantitative approaches to amenability 608
18.10. Summary of equivalent definitions of amenability 612
18.11. Amenable hierarchy 613
Chapter 19. Ultralimits, fixed-point properties, proper actions 615
19.1. Classes of Banach spaces stable with respect to ultralimits 615
19.2. Limit actions and point-selection theorem 620
19.3. Properties for actions on Hilbert spaces 625
19.4. Kazhdan’s Property (T) and the Haagerup Property 627
19.5. Groups acting non-trivially on trees do not have Property (T) 633
19.6. Property FH, a-T-menability, and group actions
on median spaces 636
19.7. Fixed-point property and proper actions for Lp-spaces 639
19.8. Groups satisfying Property (T) and the spectral gap 641
19.9. Failure of quasiisometric invariance of Property (T) 643
19.10. Summary of examples 644
Chapter 20. The Stallings Theorem and accessibility 647
20.1. Maps to trees and hyperbolic metrics on 2-dimensional
simplicial complexes 647
20.2. Transversal graphs and Dunwoody tracks 652
20.3. Existence of minimal Dunwoody tracks 656
20.4. Properties of minimal tracks 659
20.4.1. Stationarity 659
20.4.2. Disjointness of essential minimal tracks 661
20.5. The Stallings Theorem for almost finitely presented groups 664
20.6. Accessibility 666
20.7. QI rigidity of virtually free groups and free products 671
Chapter 21. Proof of Stallings’ Theorem using harmonic functions 675
21.1. Proof of Stallings’ Theorem 677
21.2. Non-amenability 681
21.3. An existence theorem for harmonic functions 683
21.4. Energy of minimum and maximum of two smooth functions 686
21.5. A compactness theorem for harmonic functions 687
21.5.1. Positive energy gap implies existence of an energy minimizer 687
21.5.2. Some coarea estimates 690
21.5.3. Energy comparison in the case of a linear isoperimetric
inequality 692
21.5.4. Proof of positivity of the energy gap 694
Chapter 22. Quasiconformal mappings 697
22.1. Linear algebra and eccentricity of ellipsoids 698
22.2. Quasisymmetric maps 699
22.3. Quasiconformal maps 701
22.4. Analytical properties of quasiconformal mappings 702
22.4.1. Some notions and results from real analysis 702
22.4.2. Differentiability properties of quasiconformal mappings 705
22.5. Quasisymmetric maps and hyperbolic geometry 712
xn
CONTENTS
Chapter 23. Groups quasiisometric to HP 717
23.1. Uniformly qu as icon formal groups 718
23.2. Hyperbolic extension of uniformly quasiconformal groups 719
23.3. Least volume ellipsoids 720
23.4. Invariant measurable conformal structure 721
23.5. Quasiconforrnality in dimension 2 724
23.5.1. Beltrami equation 724
23.5.2. Measurable Riemannian metrics 725
23.6. Proof of Tukia’s Theorem on uniformly quasiconformal groups 726
23.7. QI rigidity for surface groups 729
Chapter 24. Quasiisometries of non-uniform lattices in HP 733
24.1. Coarse topology of truncated hyperbolic spaces 734
24.2. Hyperbolic extension 738
24.3. Mostow Rigidity Theorem 739
24.4. Zooming in 743
24.5. Inverted linear mappings 745
24.6. Scattering 748
24.7. Schwartz Rigidity Theorem 750
Chapter 25. A survey of quasiisometric rigidity 753
25.1. Rigidity of symmetric spaces, lattices and hyperbolic groups 753
25.1.1. Uniform lattices 753
25.1.2. Non-uniform lattices 754
25.1.3. Symmetric spaces with Euclidean de Rham factors
and Lie groups with nilpotent normal subgroups 756
25.1.4. QI rigidity for hyperbolic spaces and groups 757
25.1.5. Failure of QI rigidity 760
25.1.6. Rigidity of random groups 762
25.2. Rigidity of relatively hyperbolic groups 762
25.3. Rigidity of classes of amenable groups 764
25.4. Bi-Lipschitz vs. quasiisometric 767
25.5. Various other QI rigidity results and problems 769
Chapter 26. Appendix by Bogdan Nica: Three theorems on linear groups 777
26.1. Introduction 777
26.2. Virtual and residual properties of groups 778
26.3. Platonov’s Theorem 778
26.4. Proof of Platonov’s Theorem 780
26.5. The Idernpotent Conjecture for linear groups 782
26.6. Proof of Formanek’s criterion 783
26.7. Notes 785
Bibliography 787
Index 813 |
| any_adam_object | 1 |
| author | Druţu, Cornelia 1967- Kapovich, Michael 1963- |
| author2 | Nica, Bogdan 1977- |
| author2_role | ctb |
| author2_variant | b n bn |
| author_GND | (DE-588)1035530821 (DE-588)134100409 (DE-588)1156786754 |
| author_facet | Druţu, Cornelia 1967- Kapovich, Michael 1963- Nica, Bogdan 1977- |
| author_role | aut aut |
| author_sort | Druţu, Cornelia 1967- |
| author_variant | c d cd m k mk |
| building | Verbundindex |
| bvnumber | BV044377523 |
| classification_rvk | SK 260 |
| ctrlnum | (OCoLC)1027719640 (DE-599)BVBBV044377523 |
| discipline | Mathematik |
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| id | DE-604.BV044377523 |
| illustrated | Illustrated |
| indexdate | 2024-11-29T15:01:49Z |
| institution | BVB |
| isbn | 9781470411046 1470411040 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029779784 |
| oclc_num | 1027719640 |
| open_access_boolean | |
| owner | DE-29T DE-188 DE-384 DE-11 DE-20 DE-19 DE-BY-UBM DE-739 DE-355 DE-BY-UBR DE-83 |
| owner_facet | DE-29T DE-188 DE-384 DE-11 DE-20 DE-19 DE-BY-UBM DE-739 DE-355 DE-BY-UBR DE-83 |
| physical | xx, 819 Seiten Illustrationen, Diagramme |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | American Mathematical Society: Colloquium publications |
| series2 | American Mathematical Society: Colloquium publications |
| spelling | Druţu, Cornelia 1967- (DE-588)1035530821 aut Geometric group theory Cornelia Druţu ; Michael Kapovich ; with an appendix by Bogdan Nica Providence, Rhode Island American Mathematical Society [2018] © 2018 xx, 819 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Colloquium publications Volume 63 Geometrische Gruppentheorie (DE-588)4651615-3 gnd rswk-swf Geometric group theory Group theory Group theory and generalizations / Special aspects of infinite or finite groups / Geometric group theory Group theory and generalizations / Special aspects of infinite or finite groups / Hyperbolic groups and nonpositively curved groups Group theory and generalizations / Special aspects of infinite or finite groups / Asymptotic properties of groups Group theory and generalizations / Special aspects of infinite or finite groups / Generators, relations, and presentations Group theory and generalizations / Special aspects of infinite or finite groups / Solvable groups, supersolvable groups Group theory and generalizations / Special aspects of infinite or finite groups / Nilpotent groups Group theory and generalizations / Special aspects of infinite or finite groups / Fundamental groups and their automorphisms Group theory and generalizations / Structure and classification of infinite or finite groups / Groups acting on trees Group theory and generalizations / Structure and classification of infinite or finite groups / Residual properties and generalizations; residually finite groups Manifolds and cell complexes / Low-dimensional topology / Topological methods in group theory Geometrische Gruppentheorie (DE-588)4651615-3 s DE-604 Kapovich, Michael 1963- (DE-588)134100409 aut Nica, Bogdan 1977- (DE-588)1156786754 ctb Erscheint auch als Online-Ausgabe 978-1-4704-4164-7 American Mathematical Society: Colloquium publications Volume 63 (DE-604)BV035417609 63 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029779784&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Druţu, Cornelia 1967- Kapovich, Michael 1963- Geometric group theory American Mathematical Society: Colloquium publications Geometrische Gruppentheorie (DE-588)4651615-3 gnd |
| subject_GND | (DE-588)4651615-3 |
| title | Geometric group theory |
| title_auth | Geometric group theory |
| title_exact_search | Geometric group theory |
| title_full | Geometric group theory Cornelia Druţu ; Michael Kapovich ; with an appendix by Bogdan Nica |
| title_fullStr | Geometric group theory Cornelia Druţu ; Michael Kapovich ; with an appendix by Bogdan Nica |
| title_full_unstemmed | Geometric group theory Cornelia Druţu ; Michael Kapovich ; with an appendix by Bogdan Nica |
| title_short | Geometric group theory |
| title_sort | geometric group theory |
| topic | Geometrische Gruppentheorie (DE-588)4651615-3 gnd |
| topic_facet | Geometrische Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029779784&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035417609 |
| work_keys_str_mv | AT drutucornelia geometricgrouptheory AT kapovichmichael geometricgrouptheory AT nicabogdan geometricgrouptheory |