Four-manifolds, geometries and knots:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Geometry & Topology Publ.
Coventry, UK
2002
|
| Schriftenreihe: | Geometry & topology monographs / Mathematics Institute, University of Warwick
5 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 379 S. |
Internformat
MARC
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| 245 | 1 | 0 | |a Four-manifolds, geometries and knots |c J. A. Hillman |
| 246 | 1 | 3 | |a Four manifolds, geometries and knots |
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Datensatz im Suchindex
| _version_ | 1804133187841949696 |
|---|---|
| adam_text | QEOMETRY & TOPOLOGY MONOGRAPHS VOLUME 5 (2002) FOUR-MANIFOLDS,
GEOMETRIES AND KNOTS J.A.HLLLMAN THE UNIVERSITY OF SYDNEY
JONH@MATHS.USYD.EDU.AU SUB GOTTINGEN 7 217 404 820 1 CONTENTS III
CONTENTS CONTENTS (III) PREFACE (IX) ACKNOWLEDGEMENT PART I : MANIFOLDS
AND PZ)-COMPLEXES 1 CHAPTER 1: GROUP THEORETIC PRELIMINARIES 3 1.1 GROUP
THEORETIC NOTATION AND TERMINOLOGY 3 1.2 MATRIX GROUPS 5 1.3 THE
HIRSCH-PLOTKIN RADICAL 6 1.4 AMENABLE GROUPS 8 1.5 HIRSCH LENGTH 10 1.6
MODULES AND FINITENESS CONDITIONS 13 1.7 ENDS AND COHOMOLOGY WITH FREE
COEFFICIENTS 16 1.8 POINCARE DUALITY GROUPS 20 1.9 HILBERT MODULES 22
CHAPTER 2: 2-COMPLEXES AND PD3 -COMPLEXES 25 2.1 NOTATION 25 2.2 L 2
-BETTI NUMBERS 26 2.3 2-COMPLEXES AND FINITELY PRESENTABLE GROUPS 28 2.4
POINCARE DUALITY 32 2.5 PD 3 -COMPLEXES 33 2.6 THE SPHERICAL CASES 35
2.7 P.D3-GROUPS 37 2.8 SUBGROUPS OF PD3 -GROUPS AND 3-MANIFOLD GROUPS 42
2.9 TT 2 (P) AS A Z[7R]-MODULE 44 CHAPTER 3: HOMOTOPY INVARIANTS OF PD4
-COMPLEXES 47 3.1 HOMOTOPY EQUIVALENCE AND ASPHERICITY 47 3.2 FINITELY
DOMINATED COVERING SPACES 53 3.3 MINIMIZING THE EULER CHARACTERISTIC 57
3.4 EULER CHARACTERISTIC 0 63 QEOMETRY & TOPOLOGY MONOGRAPHS, VOLUME 5
(2002) IV CONTENTS CHAPTER 4: MAPPING TORI AND CIRCLE BUNDLES 69 4.1
SOME NECESSARY CONDITIONS 69 4.2 CHANGE OF RINGS AND CUP PRODUCTS 71 4.3
THE CASE V = L 74 4.4 DUALITY IN INFINITE CYCLIC COVERS 75 4.5 HOMOTOPY
MAPPING TORI 76 4.6 PRODUCTS 82 4.7 SUBNORMAL SUBGROUPS 83 4.8 CIRCLE
BUNDLES 84 CHAPTER 5: SURFACE BUNDLES 89 5.1 SOME GENERAL RESULTS 89 5.2
BUNDLES WITH BASE AND FIBRE ASPHERICAL SURFACES 91 5.3 BUNDLES WITH
ASPHERICAL BASE AND FIBRE S 2 OR RP 2 96 5.4 BUNDLES OVER S 2 102 5.5
BUNDLES OVER RP 2 105 5.6 BUNDLES OVER RP 2 WITH D = 0 107 CHAPTER 6:
SIMPLE HOMOTOPY TYPE AND SURGERY ILL 6.1 THE WHITEHEAD GROUP 112 6.2 THE
S-COBORDISM STRUCTURE SET 116 6.3 STABILIZATION AND /I-COBORDISM 121 6.4
MANIFOLDS WITH TTI ELEMENTARY AMENABLE AND % = 0 122 6.5 BUNDLES OVER
ASPHERICAL SURFACES 125 PART II : 4-DIMENSIONAL GEOMETRIES 129 CHAPTER
7: GEOMETRIES AND DECOMPOSITIONS 131 7.1 GEOMETRIES 132 7.2
INFRANILMANIFOLDS 133 7.3 INFRASOLVMANIFOLDS 135 7.4 GEOMETRIC
DECOMPOSITIONS 138 7.5 ORBIFOLD BUNDLES 141 7.6 REALIZATION OF VIRTUAL
BUNDLE GROUPS 142 7.7 SEIFERT FIBRATIONS : 144 QEOMETRY & TOPOLOGY
MONOGRAPHS, VOLUME 5 (2002) CONTENTS V 7.8 COMPLEX SURFACES AND RELATED
STRUCTURES 146 CHAPTER 8: SOLVABLE LIE GEOMETRIES 151 8.1 THE
CHARACTERIZATION 151 8.2 FLAT 3-MANIFOLD GROUPS AND THEIR AUTOMORPHISMS
153 8.3 FLAT 4-MANIFOLD GROUPS WITH INFINITE ABELIANIZATION 157 8.4 FLAT
4-MANIFOLD GROUPS WITH FINITE ABELIANIZATION 161 8.5 DISTINGUISHING
BETWEEN THE GEOMETRIES 164 8.6 MAPPING TORI OF SELF HOMEOMORPHISMS OF E
3 -MANIFOLDS 165 8.7 MAPPING TORI OF SELF HOMEOMORPHISMS OF NIL 3
-MANIFOLDS 167 8.8 MAPPING TORI OF SELF HOMEOMORPHISMS OF §O 3
-MANIFOLDS 171 8.9 REALIZATION AND CLASSIFICATION 173 8.10
DIFFEOMORPHISM 175 CHAPTER 9: THE OTHER ASPHERICAL GEOMETRIES 179 9.1
ASPHERICAL SEIFERT FIBRED 4-MANIFOLDS 179 9.2 THE SEIFERT GEOMETRIES: TF
XE 2 AND SLXE 1 182 9.3 H 3 X E 1 -MANIFOLDS 185 9.4 MAPPING TORI 186
9.5 THE SEMISIMPLE GEOMETRIES: BPXTF.TF AND H 2 (C) 187 9.6 MISCELLANY
193 CHAPTER 10: MANIFOLDS COVERED BY S 2 X R 2 195 10.1 FUNDAMENTAL
GROUPS 195 10.2 HOMOTOPY TYPE 196 10.3 BUNDLE SPACES ARE GEOMETRIC 201
10.4 FUNDAMENTAL GROUPS OF S 2 X E 2 -MANIFOLDS 206 10.5 HOMOTOPY TYPES
OF S 2 X E 2 -MANIFOLDS 208 10.6 SOME REMARKS ON THE HOMEOMORPHISM TYPES
214 CHAPTER 11: MANIFOLDS COVERED BY S 3 X R 217 11.1 INVARIANTS FOR THE
HOMOTOPY TYPE 217 11.2 THE ACTION OF -K/F ON F 220 11.3 EXTENSIONS OF D
223 11.4 S 3 X E 1 -MANIFOLDS 224 QEOMETRY & TOPOLOGY MONOGRAPHS, VOLUME
5 (2002) VI CONTENTS 11.5 REALIZATION OF THE GROUPS 226 11.6 T- AND
JT6-BUNDLES OVER RP 2 WITH 9 ^ 0 228 11.7 SOME REMARKS ON THE
HOMEOMORPHISM TYPES 231 CHAPTER 12: GEOMETRIES WITH COMPACT MODELS 233
12.1 THE GEOMETRIES S 4 AND OP 2 234 12.2 THE GEOMETRY S 2 X S 2 235
12.3 BUNDLE SPACES 236 12.4 COHOMOLOGY AND STIEFEL-WHITNEY CLASSES 238
12.5 THE ACTION OF T T ON TT 2 (M) 239 12.6 HOMOTOPY TYPE 241 12.7.
SURGERY 244 CHAPTER 13: GEOMETRIC DECOMPOSITIONS OF BUNDLE SPACES 247
13.1 MAPPING TORI 247 13.2 SURFACE BUNDLES AND GEOMETRIES 252 13.3
GEOMETRIC DECOMPOSITIONS OF TORUS BUNDLES 256 13.4 COMPLEX SURFACES AND
FIBRATIONS 257 13.5 S 1 -ACTIONS AND FOLIATIONS BY CIRCLES 261 13.6
SYMPLECTIC STRUCTURES 263 PART III : 2-KNOTS 265 CHAPTER 14: KNOTS AND
LINKS 267 14.1 KNOTS 267 14.2 COVERING SPACES 269 14.3 SUMS,
FACTORIZATION AND SATELLITES 270 14.4 SPINNING AND TWIST SPINNING 271
14.5 RIBBON AND SLICE KNOTS 272 14.6 THE KERVAIRE CONDITIONS 273 14.7
WEIGHT ELEMENTS, CLASSES AND ORBITS 275 14.8 THE COMMUTATOR SUBGROUP 276
14.9 DEFICIENCY AND GEOMETRIC DIMENSION 279 14.10 ASPHERICITY 281 14.11
LINKS 282 14.12 LINK GROUPS 286 QEOMETRY & TOPOLOGY MONOGRAPHS, VOLUME 5
(2002) CONTENTS VII 14.13 HOMOLOGY SPHERES 288 CHAPTER 15: RESTRAINED
NORMAL SUBGROUPS 291 15.1 THE GROUP $ 291 15.2 ALMOST COHERENT,
RESTRAINED AND LOCALLY VIRTUALLY INDICABLE 293 15.3 ABELIAN NORMAL
SUBGROUPS 296 15.4 FINITE COMMUTATOR SUBGROUP 299 15.5 THE TITS
ALTERNATIVE 302 15.6 ABELIAN HNN BASES 302 15.7 LOCALLY FINITE NORMAL
SUBGROUPS 304 CHAPTER 16: ABELIAN NORMAL SUBGROUPS OF RANK 2 307 16.1
THE BRIESKORN MANIFOLDS M(P, Q,R) 307 16.2 RANK 2 SUBGROUPS 308 16.3
TWIST SPINS OF TORUS KNOTS 310 16.4 SOLVABLE PZ 4 -GROUPS 314 CHAPTER
17: KNOT MANIFOLDS AND GEOMETRIES 323 17.1 HOMOTOPY CLASSIFICATION OF
M(K) 323 17.2 SURGERY 324 17.3 THE ASPHERICAL CASES 325 17.4 QUASIFIBRES
AND MINIMAL SEIFERT HYPERSURFACES 327 17.5 THE SPHERICAL CASES 328 17.6
FINITE GEOMETRIC DIMENSION 2 329 17.7 GEOMETRIC 2-KNOT MANIFOLDS 332
17.8 COMPLEX SURFACES AND 2-KNOT MANIFOLDS 334 CHAPTER 18: REFLEXIVITY
337 18.1 REFLEXIVITY FOR FIBRED 2-KNOTS 337 18.2 CAPPELL-SHANESON KNOTS
340 18.3 NIL 3 -FIBRED KNOTS 343 18.4 OTHER GEOMETRICALLY FIBRED KNOTS
347 BIBLIOGRAPHY 353 INDEX 375 QEOMETRY & TOPOLOGY MONOGRAPHS, VOLUME 5
(2002)
|
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| discipline | Mathematik |
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| physical | XIII, 379 S. |
| publishDate | 2002 |
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| series2 | Geometry & topology monographs / Mathematics Institute, University of Warwick |
| spelling | Four-manifolds, geometries and knots J. A. Hillman Four manifolds, geometries and knots Geometry & Topology Publ. Coventry, UK 2002 XIII, 379 S. txt rdacontent n rdamedia nc rdacarrier Geometry & topology monographs / Mathematics Institute, University of Warwick 5 Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Dimension 4 (DE-588)4338676-3 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Dimension 4 (DE-588)4338676-3 s DE-604 Hillman, Jonathan 1947- Sonstige (DE-588)1031495649 oth Mathematics Institute, University of Warwick Geometry & topology monographs 5 (DE-604)BV019727192 5 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013054413&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Four-manifolds, geometries and knots Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 4 (DE-588)4338676-3 gnd |
| subject_GND | (DE-588)4037379-4 (DE-588)4338676-3 |
| title | Four-manifolds, geometries and knots |
| title_alt | Four manifolds, geometries and knots |
| title_auth | Four-manifolds, geometries and knots |
| title_exact_search | Four-manifolds, geometries and knots |
| title_full | Four-manifolds, geometries and knots J. A. Hillman |
| title_fullStr | Four-manifolds, geometries and knots J. A. Hillman |
| title_full_unstemmed | Four-manifolds, geometries and knots J. A. Hillman |
| title_short | Four-manifolds, geometries and knots |
| title_sort | four manifolds geometries and knots |
| topic | Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 4 (DE-588)4338676-3 gnd |
| topic_facet | Mannigfaltigkeit Dimension 4 |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013054413&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019727192 |
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