Algebraic models in geometry:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2008
|
| Edition: | 1. publ. |
| Series: | Oxford graduate texts in mathematics
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 460 S. |
| ISBN: | 9780199206520 9780199206513 |
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MARC
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| 020 | |a 9780199206513 |9 978-0-19-920651-3 | ||
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| 100 | 1 | |a Félix, Yves |d 1951- |e Verfasser |0 (DE-588)111765560 |4 aut | |
| 245 | 1 | 0 | |a Algebraic models in geometry |c Yves Félix ; John Oprea ; Daniel Tanré |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2008 | |
| 300 | |a XXI, 460 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Oxford graduate texts in mathematics |v 17 | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Homotopy theory | |
| 650 | 0 | 7 | |a Algebraisches Modell |0 (DE-588)4141857-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
| 689 | 0 | 1 | |a Algebraisches Modell |0 (DE-588)4141857-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Oprea, John |e Verfasser |4 aut | |
| 700 | 1 | |a Tanré, Daniel |e Verfasser |4 aut | |
| 830 | 0 | |a Oxford graduate texts in mathematics |v 17 |w (DE-604)BV011416591 |9 17 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016278413&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016278413 | ||
Record in the Search Index
| _version_ | 1804137320465563648 |
|---|---|
| adam_text | Contents
Preface
vii
1
Lie groups and homogeneous spaces
1
1.1
Lie groups
2
1.2
Lie algebras
3
1.3
Lie groups and Lie algebras
5
1.4
Abelian Lie groups
8
1.5
Classical examples of Lie groups
8
1.5.1
Subgroups of the real linear group
9
1.5.2
Subgroups of the complex linear group
10
1.5.3
Subgroups of the quatemionic linear group
10
1.6
Invariant forms
11
1.7
Cohomology of Lie groups
16
1.8
Simple and
semisimple
compact connected
Lie groups
21
1.9
Homogeneous spaces
26
1.10
Principal bundles
32
1.11
Classifying spaces of Lie groups
38
1.12 Stiefel
and
Grassmann
manifolds
42
1.13
The Cartan-Weil model
47
2
Minimal models
56
2.1
Commutative differential graded algebras
57
2.2
Homotopy between morphisms of cdga s
61
2.3
Models in algebra
64
2.3.1
Minimal models of cdga s and morphisms
64
2.3.2
Relative minimal models
66
2.4
Models of spaces
67
2.4.1
Real and rational minimal models
67
2.4.2
Construction of APL(X)
69
Contents
2.4.3
Examples of
minimal modeis
oí
spaces
71
2.4.4
Other models for spaces
74
2.5
Minimal models and homotopy theory
75
2.5.1
Minimal models and homotopy groups
75
2.5.2
Relative minimal model of a fibration
78
2.5.3
The dichotomy theorem
84
2.5.4
Minimal models and some homotopy constructions
87
2.6
Realizing minimal cdga s as spaces
90
2.6.1
Topological realization of a minimal cdga
90
2.6.2
The cochains on a graded Lie algebra
91
2.7
Formality
92
2.7.1
Bigraded model
95
2.7.2
Obstructions to formality
96
2.8
Semifree models
100
3
Manifolds
104
3.1
Minimal models and manifolds
105
3.1.1
Sullivan-Barge classification
105
3.1.2
The rational homotopy groups of a manifold
106
3.1.3
Poincaré
duality models
109
3.1.4
Formality of manifolds
110
3.2
Nilmanlfolds
116
3.2.1
Relations with Lie algebras
117
3.2.2
Relations with principal bundles
121
3.3
Finite group actions
123
3.3.1
An equivariant model for
Г-ѕрасеѕ
123
3.3.2
Weyl group and cohomology of BG
127
3.4
Biquotients
133
3.4.1
Definitions and properties
133
3.4.2
Models of biquotients
137
3.5
The canonical model of a Riemannian manifold
139
4
Complex and symplectic manifolds
145
4.1
Complex and almost complex manifolds
148
4.1.1
Complex manifolds
148
4.1.2
Almost complex manifolds
150
4.1.3
Differential forms on an almost
complex manifold
152
4.1.4
Integrability of almost complex manifolds
154
Contents
4.2 Kahler
manifolds
156
4.2.1
Definitions and properties
156
4.2.2
Examples: Calabi-Eckmann manifolds
159
4.2.3
Topology of compact
Kahler
manifolds
162
4.3
The Dolbeault model of a complex manifold
168
4.3.1
Definition and existence
169
4.3.2
The Dolbeault model of
a
Kahler
manifold
172
4.3.3
The
Borei
spectral sequence
173
4.3.4
The Dolbeault model of Calabi-Eckmann
manifolds
175
4.4
The
Frölicher
spectral sequence
178
4.4.1
Definition and properties
178
4.4.2
Pittie s examples
179
4.5
Symplectic manifolds
182
4.5.1
Definition of symplectic manifold
182
4.5.2
Examples of symplectic manifolds
183
4.5.3
Symplectic manifolds and the hard
Lefschetz property
184
4.5.4
Symplectic and complex manifolds
187
4.6
Cohomologically symplectic manifolds
187
4.6.1
C-symplectic manifolds
187
4.6.2
Symplectic homogeneous spaces and
biquotients
188
4.6.3
Symplectic fibrations
189
4.6.4
Symplectic nilmanifolds
191
4.6.5
Homotopy of
nilpotent
symplectic manifolds
194
4.7
Appendix: Complex and symplectic linear algebra
196
4.7.1
Complex structure on a real vector space
196
4.7.2
Complexification of a complex structure
197
4.7.3
Hermitian products
198
4.7.4
Symplectic linear algebra
200
4.7.5
Symplectic and complex linear algebra
201
4.7.6
Generalized complex structure
202
5
Geodesies
205
5.1
The closed geodesic problem
207
5.2
A model for the free loop space
210
5.3
A solution to the closed geodesic problem
213
5.4
A-invariant
closed geodesies
215
5.5
Existence of infinitely many
A-invariant
geodesies
222
Contents
5.6
Gromov s estimate and the growth of
closed geodesies
223
5.7
The topological entropy
227
5.8
Manifolds whose geodesies are closed
232
5.9
Bar construction,
Hochschild homology
and cohomology
234
6
Curvature
239
6.1
Introduction: Recollections on curvature
239
6.2
Grove s question
243
6.2.1
The Fang-Rong approach
243
6.2.2
Totaro s approach
249
6.3
Vampiric
vector bundles
252
6.3.1
The examples of
Özaydin
and Walschap
253
6.3.2
The method of Belegradek and Kapovitch
259
6.4
Final thoughts
265
6.5
Appendix
266
7
G-spaces
271
7.1
Basic definitions and results
273
7.2
The
Borei
fibration
275
7.3
The
toral
rank
276
7.3.1
Toral
rank for rationally elliptic spaces
278
7.3.2
Computation of rkn(M) with minimal models
280
7.3.3
The
toral
rank conjecture
283
7.3.4
Toral
rank and center of
3Γ*(ΩΜ)®
Q
287
7.3.5
The TRC for Lie algebras
289
7.4
The localization theorem
291
7.4.1
Relations between G-manifold and fixed set
292
7.4.2
Some examples
295
7.5
The rational homotopy of a fixed point set component
298
7.5.1
The rational homotopy groups of a component
298
7.5.2
Presentation of the Lie algebra Lp
=
jr*
(ΩΡ)
®
Q
303
7.5.3
Z/lZ-Sullivan models
305
7.6
Hamiltonian actions and bundles
306
7.6.1
Basic definitions and properties
306
7.6.2
Hamiltonian and cohomologically free actions
308
7.6.3
The symplectic
toral
rank theorem
312
7.6.4
Some properties of Hamiltonian actions
312
7.6.5
Hamiltonian bundles
314
Contents
8 Blow-ups and
Intersection
Products 317
8.1
8.2
8.3
8.4
The model of the complement of a submanifold
318
8.1.1
Shriek maps
319
8.1.2
Algebraic mapping cones
321
8.1.3
The model for the complement
С
324
8.1.4
Properties of
Poincaré
duality models
328
8.1.5
The configuration space of two points in
a manifold
329
Symplectic blow-ups
330
8.2.1
Complex blow-ups
331
8.2.2
Blowing up along a submanifold
332
A model for a symplectic blow-up
334
8.3.1
The basic pullback diagram of PL-forms
334
8.3.2
An illustrative example
334
8.3.3
The model for the blow-up
335
8.3.4
McDuff s example
337
8.3.5
Effect of the symplectic form on the blow-up
339
8.3.6
Vanishing of Chern classes for KT
339
The Chas-Sullivan loop product on loop space
homology
341
8.4.1
The classical intersection product
341
8.4.2
The Chas-Sullivan loop product
342
8.4.3
A rational model for the loop product
344
8.4.4
Hochschild cohomology
and Cohen-Jones
theorem
346
8.4.5
The Chas-Sullivan loop product and
closed geodesies
348
9
A Florilège
of geometric applications
350
9.1
Configuration spaces
351
9.1.1
The Fadell-Neuwirth fibrations
352
9.1.2
The rational homotopy of configuration spaces
353
9.1.3
The configuration spaces F(R ,k)
354
9.1.4
The configuration spaces of
a projective
manifold
355
9.2
Arrangements
358
9.2.1
Formality of the complement of a geometric
lattice
361
9.2.2
Rational hyperbolicity of the space M(A)
362
Contents
9.3 Toric
topology
363
9.4
Complex smooth algebraic varieties
364
9.5
Spaces of sections and Gelfand-Fuchs cohomology
367
9.5.1
The Haefliger model for spaces of sections
367
9.5.2
The Bousfield-Peterson-Smith model
371
9.5.3
Configuration spaces and spaces of sections
373
9.5.4
Gelfand-Fuchs cohomology
375
9.6
Iterated integrals
376
9.6.1
Definition of iterated integrals
376
9.6.2
The cdga of iterated integrals
379
9.6.3
Iterated integrals and the double bar
construction
381
9.6.4
Iterated integrals, the
Hochschild
complex and
the free loop space
384
9.6.5
Formal homology connection and holonomy
385
9.6.6
A topological application
387
9.7
Cohomological conjectures
388
9.7.1
The
toral
rank conjecture
388
9.7.2
The Halperin conjecture
388
9.7.3
The
Bott
conjecture
389
9.7.4
The Gromov conjecture on LM
390
9.7.5
The Lalonde-McDuff question
390
A De Rham
forms
392
A.1 Differential forms
392
A.2 Operators on forms
398
A.3 The
de Rham
theorem
402
A.4 The Hodge decomposition
404
В
Spectral sequences
409
B.1 What is a spectral sequence?
409
B.2 Spectral sequences in cohomology
411
B.3 Spectral sequences and nitrations
412
B.4
Serre
spectral sequence
413
B.5 Zeeman-Moore theorem
416
B.6 An algebraic example: The odd spectral
sequence
419
B.7 A particular case: A double complex
420
Contents
С
Basic homotopy
recollections
423
C.1
и
-equivalences
and homotopy
sets
423
C.2 Homotopy pushouts and pullbacks 424
C.3 Cofibrations and fibrations 428
References
433
Index 451
|
| adam_txt |
Contents
Preface
vii
1
Lie groups and homogeneous spaces
1
1.1
Lie groups
2
1.2
Lie algebras
3
1.3
Lie groups and Lie algebras
5
1.4
Abelian Lie groups
8
1.5
Classical examples of Lie groups
8
1.5.1
Subgroups of the real linear group
9
1.5.2
Subgroups of the complex linear group
10
1.5.3
Subgroups of the quatemionic linear group
10
1.6
Invariant forms
11
1.7
Cohomology of Lie groups
16
1.8
Simple and
semisimple
compact connected
Lie groups
21
1.9
Homogeneous spaces
26
1.10
Principal bundles
32
1.11
Classifying spaces of Lie groups
38
1.12 Stiefel
and
Grassmann
manifolds
42
1.13
The Cartan-Weil model
47
2
Minimal models
56
2.1
Commutative differential graded algebras
57
2.2
Homotopy between morphisms of cdga's
61
2.3
Models in algebra
64
2.3.1
Minimal models of cdga's and morphisms
64
2.3.2
Relative minimal models
66
2.4
Models of spaces
67
2.4.1
Real and rational minimal models
67
2.4.2
Construction of APL(X)
69
Contents
2.4.3
Examples of
minimal modeis
oí
spaces
71
2.4.4
Other models for spaces
74
2.5
Minimal models and homotopy theory
75
2.5.1
Minimal models and homotopy groups
75
2.5.2
Relative minimal model of a fibration
78
2.5.3
The dichotomy theorem
84
2.5.4
Minimal models and some homotopy constructions
87
2.6
Realizing minimal cdga's as spaces
90
2.6.1
Topological realization of a minimal cdga
90
2.6.2
The cochains on a graded Lie algebra
91
2.7
Formality
92
2.7.1
Bigraded model
95
2.7.2
Obstructions to formality
96
2.8
Semifree models
100
3
Manifolds
104
3.1
Minimal models and manifolds
105
3.1.1
Sullivan-Barge classification
105
3.1.2
The rational homotopy groups of a manifold
106
3.1.3
Poincaré
duality models
109
3.1.4
Formality of manifolds
110
3.2
Nilmanlfolds
116
3.2.1
Relations with Lie algebras
117
3.2.2
Relations with principal bundles
121
3.3
Finite group actions
123
3.3.1
An equivariant model for
Г-ѕрасеѕ
123
3.3.2
Weyl group and cohomology of BG
127
3.4
Biquotients
133
3.4.1
Definitions and properties
133
3.4.2
Models of biquotients
137
3.5
The canonical model of a Riemannian manifold
139
4
Complex and symplectic manifolds
145
4.1
Complex and almost complex manifolds
148
4.1.1
Complex manifolds
148
4.1.2
Almost complex manifolds
150
4.1.3
Differential forms on an almost
complex manifold
152
4.1.4
Integrability of almost complex manifolds
154
Contents
4.2 Kahler
manifolds
156
4.2.1
Definitions and properties
156
4.2.2
Examples: Calabi-Eckmann manifolds
159
4.2.3
Topology of compact
Kahler
manifolds
162
4.3
The Dolbeault model of a complex manifold
168
4.3.1
Definition and existence
169
4.3.2
The Dolbeault model of
a
Kahler
manifold
172
4.3.3
The
Borei
spectral sequence
173
4.3.4
The Dolbeault model of Calabi-Eckmann
manifolds
175
4.4
The
Frölicher
spectral sequence
178
4.4.1
Definition and properties
178
4.4.2
Pittie's examples
179
4.5
Symplectic manifolds
182
4.5.1
Definition of symplectic manifold
182
4.5.2
Examples of symplectic manifolds
183
4.5.3
Symplectic manifolds and the hard
Lefschetz property
184
4.5.4
Symplectic and complex manifolds
187
4.6
Cohomologically symplectic manifolds
187
4.6.1
C-symplectic manifolds
187
4.6.2
Symplectic homogeneous spaces and
biquotients
188
4.6.3
Symplectic fibrations
189
4.6.4
Symplectic nilmanifolds
191
4.6.5
Homotopy of
nilpotent
symplectic manifolds
194
4.7
Appendix: Complex and symplectic linear algebra
196
4.7.1
Complex structure on a real vector space
196
4.7.2
Complexification of a complex structure
197
4.7.3
Hermitian products
198
4.7.4
Symplectic linear algebra
200
4.7.5
Symplectic and complex linear algebra
201
4.7.6
Generalized complex structure
202
5
Geodesies
205
5.1
The closed geodesic problem
207
5.2
A model for the free loop space
210
5.3
A solution to the closed geodesic problem
213
5.4
A-invariant
closed geodesies
215
5.5
Existence of infinitely many
A-invariant
geodesies
222
Contents
5.6
Gromov's estimate and the growth of
closed geodesies
223
5.7
The topological entropy
227
5.8
Manifolds whose geodesies are closed
232
5.9
Bar construction,
Hochschild homology
and cohomology
234
6
Curvature
239
6.1
Introduction: Recollections on curvature
239
6.2
Grove's question
243
6.2.1
The Fang-Rong approach
243
6.2.2
Totaro's approach
249
6.3
Vampiric
vector bundles
252
6.3.1
The examples of
Özaydin
and Walschap
253
6.3.2
The method of Belegradek and Kapovitch
259
6.4
Final thoughts
265
6.5
Appendix
266
7
G-spaces
271
7.1
Basic definitions and results
273
7.2
The
Borei
fibration
275
7.3
The
toral
rank
276
7.3.1
Toral
rank for rationally elliptic spaces
278
7.3.2
Computation of rkn(M) with minimal models
280
7.3.3
The
toral
rank conjecture
283
7.3.4
Toral
rank and center of
3Γ*(ΩΜ)®
Q
287
7.3.5
The TRC for Lie algebras
289
7.4
The localization theorem
291
7.4.1
Relations between G-manifold and fixed set
292
7.4.2
Some examples
295
7.5
The rational homotopy of a fixed point set component
298
7.5.1
The rational homotopy groups of a component
298
7.5.2
Presentation of the Lie algebra Lp
=
jr*
(ΩΡ)
®
Q
303
7.5.3
Z/lZ-Sullivan models
305
7.6
Hamiltonian actions and bundles
306
7.6.1
Basic definitions and properties
306
7.6.2
Hamiltonian and cohomologically free actions
308
7.6.3
The symplectic
toral
rank theorem
312
7.6.4
Some properties of Hamiltonian actions
312
7.6.5
Hamiltonian bundles
314
Contents
8 Blow-ups and
Intersection
Products 317
8.1
8.2
8.3
8.4
The model of the complement of a submanifold
318
8.1.1
Shriek maps
319
8.1.2
Algebraic mapping cones
321
8.1.3
The model for the complement
С
324
8.1.4
Properties of
Poincaré
duality models
328
8.1.5
The configuration space of two points in
a manifold
329
Symplectic blow-ups
330
8.2.1
Complex blow-ups
331
8.2.2
Blowing up along a submanifold
332
A model for a symplectic blow-up
334
8.3.1
The basic pullback diagram of PL-forms
334
8.3.2
An illustrative example
334
8.3.3
The model for the blow-up
335
8.3.4
McDuff's example
337
8.3.5
Effect of the symplectic form on the blow-up
339
8.3.6
Vanishing of Chern classes for KT
339
The Chas-Sullivan loop product on loop space
homology
341
8.4.1
The classical intersection product
341
8.4.2
The Chas-Sullivan loop product
342
8.4.3
A rational model for the loop product
344
8.4.4
Hochschild cohomology
and Cohen-Jones
theorem
346
8.4.5
The Chas-Sullivan loop product and
closed geodesies
348
9
A Florilège
of geometric applications
350
9.1
Configuration spaces
351
9.1.1
The Fadell-Neuwirth fibrations
352
9.1.2
The rational homotopy of configuration spaces
353
9.1.3
The configuration spaces F(R",k)
354
9.1.4
The configuration spaces of
a projective
manifold
355
9.2
Arrangements
358
9.2.1
Formality of the complement of a geometric
lattice
361
9.2.2
Rational hyperbolicity of the space M(A)
362
Contents
9.3 Toric
topology
363
9.4
Complex smooth algebraic varieties
364
9.5
Spaces of sections and Gelfand-Fuchs cohomology
367
9.5.1
The Haefliger model for spaces of sections
367
9.5.2
The Bousfield-Peterson-Smith model
371
9.5.3
Configuration spaces and spaces of sections
373
9.5.4
Gelfand-Fuchs cohomology
375
9.6
Iterated integrals
376
9.6.1
Definition of iterated integrals
376
9.6.2
The cdga of iterated integrals
379
9.6.3
Iterated integrals and the double bar
construction
381
9.6.4
Iterated integrals, the
Hochschild
complex and
the free loop space
384
9.6.5
Formal homology connection and holonomy
385
9.6.6
A topological application
387
9.7
Cohomological conjectures
388
9.7.1
The
toral
rank conjecture
388
9.7.2
The Halperin conjecture
388
9.7.3
The
Bott
conjecture
389
9.7.4
The Gromov conjecture on LM
390
9.7.5
The Lalonde-McDuff question
390
A De Rham
forms
392
A.1 Differential forms
392
A.2 Operators on forms
398
A.3 The
de Rham
theorem
402
A.4 The Hodge decomposition
404
В
Spectral sequences
409
B.1 What is a spectral sequence?
409
B.2 Spectral sequences in cohomology
411
B.3 Spectral sequences and nitrations
412
B.4
Serre
spectral sequence
413
B.5 Zeeman-Moore theorem
416
B.6 An algebraic example: The odd spectral
sequence
419
B.7 A particular case: A double complex
420
Contents
С
Basic homotopy
recollections
423
C.1
и
-equivalences
and homotopy
sets
423
C.2 Homotopy pushouts and pullbacks 424
C.3 Cofibrations and fibrations 428
References
433
Index 451 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Félix, Yves 1951- Oprea, John Tanré, Daniel |
| author_GND | (DE-588)111765560 |
| author_facet | Félix, Yves 1951- Oprea, John Tanré, Daniel |
| author_role | aut aut aut |
| author_sort | Félix, Yves 1951- |
| author_variant | y f yf j o jo d t dt |
| building | Verbundindex |
| bvnumber | BV023075307 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612.7 |
| callnumber-search | QA612.7 |
| callnumber-sort | QA 3612.7 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 240 SK 340 SK 350 |
| ctrlnum | (OCoLC)254182741 (DE-599)BVBBV023075307 |
| dewey-full | 514.24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.24 |
| dewey-search | 514.24 |
| dewey-sort | 3514.24 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV023075307 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:34:50Z |
| indexdate | 2024-07-09T21:10:25Z |
| institution | BVB |
| isbn | 9780199206520 9780199206513 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016278413 |
| oclc_num | 254182741 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR DE-11 DE-20 DE-384 DE-19 DE-BY-UBM |
| owner_facet | DE-703 DE-355 DE-BY-UBR DE-11 DE-20 DE-384 DE-19 DE-BY-UBM |
| physical | XXI, 460 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | Oxford graduate texts in mathematics |
| series2 | Oxford graduate texts in mathematics |
| spelling | Félix, Yves 1951- Verfasser (DE-588)111765560 aut Algebraic models in geometry Yves Félix ; John Oprea ; Daniel Tanré 1. publ. Oxford [u.a.] Oxford Univ. Press 2008 XXI, 460 S. txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts in mathematics 17 Geometry, Algebraic Homotopy theory Algebraisches Modell (DE-588)4141857-8 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Algebraisches Modell (DE-588)4141857-8 s DE-604 Oprea, John Verfasser aut Tanré, Daniel Verfasser aut Oxford graduate texts in mathematics 17 (DE-604)BV011416591 17 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016278413&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Félix, Yves 1951- Oprea, John Tanré, Daniel Algebraic models in geometry Oxford graduate texts in mathematics Geometry, Algebraic Homotopy theory Algebraisches Modell (DE-588)4141857-8 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4141857-8 (DE-588)4001161-6 |
| title | Algebraic models in geometry |
| title_auth | Algebraic models in geometry |
| title_exact_search | Algebraic models in geometry |
| title_exact_search_txtP | Algebraic models in geometry |
| title_full | Algebraic models in geometry Yves Félix ; John Oprea ; Daniel Tanré |
| title_fullStr | Algebraic models in geometry Yves Félix ; John Oprea ; Daniel Tanré |
| title_full_unstemmed | Algebraic models in geometry Yves Félix ; John Oprea ; Daniel Tanré |
| title_short | Algebraic models in geometry |
| title_sort | algebraic models in geometry |
| topic | Geometry, Algebraic Homotopy theory Algebraisches Modell (DE-588)4141857-8 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Geometry, Algebraic Homotopy theory Algebraisches Modell Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016278413&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011416591 |
| work_keys_str_mv | AT felixyves algebraicmodelsingeometry AT opreajohn algebraicmodelsingeometry AT tanredaniel algebraicmodelsingeometry |