Embeddings in manifolds:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2009]
|
| Series: | Graduate studies in mathematics
volume 106 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvii, 468 Seiten Illustrationen, Diagramme |
| ISBN: | 9780821836972 |
Staff View
MARC
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| 020 | |a 9780821836972 |c alk. paper |9 978-0-8218-3697-2 | ||
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| 100 | 1 | |a Daverman, Robert J. |d 1941- |e Verfasser |0 (DE-588)141996625 |4 aut | |
| 245 | 1 | 0 | |a Embeddings in manifolds |c Robert J. Daverman, Gerard A. Venema |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2009] | |
| 264 | 4 | |c © 2009 | |
| 300 | |a xvii, 468 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v volume 106 | |
| 650 | 4 | |a Embeddings (Mathematics) | |
| 650 | 4 | |a Manifolds (Mathematics) | |
| 650 | 0 | 7 | |a Topologische Einbettung |0 (DE-588)4455162-9 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Graduate studies in mathematics |v volume 106 |w (DE-604)BV009739289 |9 106 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018734483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Record in the Search Index
| _version_ | 1804140854169829376 |
|---|---|
| adam_text | Contents
Acknowledgments
xi
Introduction: The Main Problem
xiii
Chapter
0.
Prequel
1
§0.1.
More definitions and notation
1
§0.2.
The Seifert-van
Kampen
Theorem
3
§0.3.
The ultimate duality theorem
б
§0.4.
The Vietoris-Begle Theorem
9
§0.5.
Higher homotopy groups
9
§0.6.
Absolute neighborhood retracts
12
§0.7.
Dimension theory
14
§0.8.
The Hurewicz Isomorphism Theorem and its localization
16
§0.9.
The Whitehead Theorem
17
§0.10.
Acyclic complexes and contractible manifolds
17
§0.11.
The 2-dimensional PL
Schönflies
Theorem
19
Chapter
1.
Tame and Knotted Embeddings
23
§1.1.
Knotted and flat piecewise linear embeddings
23
§1.2.
Tame and locally flat
topologica!
embeddings
29
§1.3.
Local co-connectedness properties
30
§1.4.
Suspending and spinning
35
vii
viii
Contents
Chapter
2.
Wild and Flat Embeddings
41
§2.1.
Antoine s necklace and Alexander s horned sphere
41
§2.2.
Function spaces
53
§2.3.
Shrinkable decompositions and the
Bing
shrinking criterion
55
§2.4.
Cellular sets and the Generalized
Schönflies
Theorem
59
§2.5.
The
Klee
trick
66
§2.6.
The product of M.1 with an arc decomposition
67
§2.7.
Everywhere wild cells and spheres
73
§2.8.
Miscellaneous examples of wild embeddings
75
§2.9.
Embeddings that are piecewise linear modulo one point
91
Chapter
3.
Engulfing, Cellularity, and Embedding Dimension
97
§3.1.
Engulfing without control
98
§3.2.
Application: The cellularity criterion
106
§3.3.
Engulfing with control
114
§3.4.
Application: Embedding dimension
123
§3.5.
Embeddings of
Menger
continua
130
§3.6.
Embedding dimension and Hausdorff dimension
136
Chapter
4.
Trivial-range Embeddings
145
§4.1.
Unknotting PL embeddings of polyhedra
146
§4.2.
Spaces of embeddings and taming of polyhedra
152
§4.3.
Taming 1-LCC embeddings of polyhedra
159
§4.4.
Unknotting 1-LCC embeddings of
compacta
161
§4.5.
Chart-by-chart analysis of topological manifolds
162
§4.6.
Detecting 1-LCC embeddings
163
§4.7.
More wild embeddings
169
§4.8.
Even more wild embeddings
172
Chapter
5.
Codimension-three Embeddings
181
§5.1.
Constructing PL embeddings of polyhedra
182
§5.2.
Constructing PL embeddings of manifolds
190
§5.3.
Unknotting PL embeddings of manifolds
196
§5.4.
Unknotting PL embeddings of polyhedra
211
§5.5.
1-LCC approximation of embeddings of
compacta
227
§5.6.
PL approximation of embeddings of manifolds
243
§5.7.
Taming 1-LCC embeddings of polyhedra
261
§5.8.
PL approximation of embeddings of polyhedra
263
Contents ix
Chapter
6. Codimension-two Embeddings 273
§6.1. Piecewise linear
knotting and algebraic unknotting
274
§6.2. Topological
flattening and algebraic knotting
283
§6.3.
Local flatness and local homotopy properties
293
§6.4.
The homology of an infinite cyclic cover
298
§6.5.
Properties of the Alexander polynomial
311
§6.6.
A topological embedding that cannot be approximated by PL
embeddings
325
§6.7.
A homotopy equivalence that is not homotopic to an
embedding
334
§6.8.
Disk bundle neighborhoods and taming
346
Chapter
7.
Codimension-one Embeddings
349
§7.1.
Codimension-one separation properties
350
§7.2.
The 1-LCC characterization of local flatness for collared
embeddings
353
§7.3.
Unknotting close 1-LCC embeddings of manifolds
358
§7.4.
The Cell-like Approximation Theorem
366
§7.5.
Determining
η
-cells by embeddings of M 1 in Sn
371
§7.6.
The 1-LCC characterization of local flatness
377
§7.7.
Locally flat approximations
382
§7.8.
Kirby-Siebenmann obstruction theory
402
§7.9.
Detecting 1-LCC embeddings
403
§7.10.
Sewings of crumpled n-cubes
410
§7.11.
Wild examples and mapping cylinder neighborhoods
417
Chapter
8.
Codimension-zero Embeddings
425
§8.1.
Manifold characterizations
425
§8.2.
The a- and ^-Approximation Theorems
427
§8.3.
Ends of manifolds
427
§8.4.
Ends of maps
432
§8.5.
Quinn s obstruction and the topological characterization of
manifolds
435
§8.6.
Exotic homology manifolds
437
§8.7.
Homotopy tori are tori
439
§8.8.
Approximating stable homeomorphisms of Rn by PL
homeomorphisms
439
χ
Contents
§8.9.
Rigidity: Homotopy equivalence implies homeomorphism
442
§8.10.
Simplicial
triangulations
443
Bibliography
445
Selected Symbols and Abbreviations
461
Index
463
|
| any_adam_object | 1 |
| author | Daverman, Robert J. 1941- |
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| dewey-full | 514 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514 |
| dewey-search | 514 |
| dewey-sort | 3514 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T22:06:35Z |
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| isbn | 9780821836972 |
| language | English |
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| physical | xvii, 468 Seiten Illustrationen, Diagramme |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Daverman, Robert J. 1941- Verfasser (DE-588)141996625 aut Embeddings in manifolds Robert J. Daverman, Gerard A. Venema Providence, Rhode Island American Mathematical Society [2009] © 2009 xvii, 468 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics volume 106 Embeddings (Mathematics) Manifolds (Mathematics) Topologische Einbettung (DE-588)4455162-9 gnd rswk-swf Topologische Einbettung (DE-588)4455162-9 s DE-604 Venema, Gerard 1949- Sonstige (DE-588)142006254 oth Erscheint auch als Online-Ausgabe 978-1-4704-1591-4 Graduate studies in mathematics volume 106 (DE-604)BV009739289 106 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018734483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Daverman, Robert J. 1941- Embeddings in manifolds Graduate studies in mathematics Embeddings (Mathematics) Manifolds (Mathematics) Topologische Einbettung (DE-588)4455162-9 gnd |
| subject_GND | (DE-588)4455162-9 |
| title | Embeddings in manifolds |
| title_auth | Embeddings in manifolds |
| title_exact_search | Embeddings in manifolds |
| title_full | Embeddings in manifolds Robert J. Daverman, Gerard A. Venema |
| title_fullStr | Embeddings in manifolds Robert J. Daverman, Gerard A. Venema |
| title_full_unstemmed | Embeddings in manifolds Robert J. Daverman, Gerard A. Venema |
| title_short | Embeddings in manifolds |
| title_sort | embeddings in manifolds |
| topic | Embeddings (Mathematics) Manifolds (Mathematics) Topologische Einbettung (DE-588)4455162-9 gnd |
| topic_facet | Embeddings (Mathematics) Manifolds (Mathematics) Topologische Einbettung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018734483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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