Simplicial structures in topology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2011
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| Series: | CMS books in mathematics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Ital. übers. |
| Physical Description: | XVI, 243 S. graph. Darst. |
| ISBN: | 9781441972354 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804145577019047936 |
|---|---|
| adam_text | Titel: Simplicial Structures in Topology
Autor: Ferrario, Davide L.
Jahr: 2011
Contents
I Fundamental Concepts......................................... 1
1.1 Topology................................................. 1
1.1.1 Topological Spaces................................... 1
1.1.2 Connectedness...................................... 9
1.1.3 Compactness........................................ 16
1.1.4 Function Spaces..................................... 22
1.1.5 Lebesgue Number................................... 24
1.2 Categories ................................................ 27
1.2.1 General Ideas on Categories........................... 27
1.2.2 Pushouts........................................... 33
1.3 Group Actions............................................. 39
II The Category of Simplicial Complexes............................ 43
II. 1 Euclidean Simplicial Complexes.............................. 43
11.2 Abstract Simplicial Complexes............................... 46
11.2.1 The Geometric Realization Functor..................... 48
11.2.2 Simplicial Complexes and Immersions.................. 56
11.2.3 The Homology Functor............................... 59
11.3 Introduction to Homological Algebra.......................... 65
11.4 Simplicial Homology....................................... 75
II.4.1 Reduced Homology.................................. 87
11.5 Homology with Coefficients ................................. 88
HI Homology of Polyhedra......................................... 99
III. 1 The Category of Polyhedra................................... 99
111.2 Homology of Polyhedra.....................................108
111.3 Some Applications.........................................117
111.4 Relative Homology for Polyhedra.............................125
111.5 Homology of Real Projective Spaces..........................128
111.5.1 Block Homology....................................131
111.5.2 Homology of EP , with ç 4.........................138
xvi Contents
IH.6 Homology of the Product of Two Polyhedra....................140
111.6.1 Acyclic Models Theorem.............................140
111.6.2 Homology of the Product of Two Polyhedra..............147
IV Cohomology...................................................151
IV.l Cohomology with Coefficients in G...........................151
IV.1.1 Cohomology of Polyhedra.............................158
IV.2 The Cohomology Ring......................................160
IV.3 The Cap Product...........................................166
V Triangulable Manifolds.........................................171
V. 1 Topological Manifolds......................................171
V.I.I Triangulable Manifolds...............................173
V.2 Closed Surfaces............................................176
V.3 Poincaré Duality...........................................189
VI Homotopy Groups.............................................195
VI.l Fundamental Group.........................................195
VI. 1.1 Fundamental Groups of Polyhedra......................199
VI. 1.2 Polyhedra with a Given Fundamental Group..............207
VI.2 Fundamental Group and Homology...........................210
VI.3 Homotopy Groups..........................................213
VI.3.1 Action of the Fundamental Group on the Higher
Homotopy Groups...................................221
VI.3.2 On the Homotopy Groups of Spheres ...................225
VI.3.3 Another Approach to Homotopy Groups.................227
VI.4 Obstruction Theory.........................................232
References.........................................................239
Index.............................................................241
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T23:21:39Z |
| institution | BVB |
| isbn | 9781441972354 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022458837 |
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| physical | XVI, 243 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
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| series2 | CMS books in mathematics |
| spelling | Ferrario, Davide L. Verfasser (DE-588)1014404460 aut Strutture simpliciali in tolopogia Simplicial structures in topology Davide L. Ferrario ; Renzo A. Piccinini New York, NY Springer 2011 XVI, 243 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier CMS books in mathematics Aus dem Ital. übers. Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 s DE-604 Piccinini, Renzo A. Sonstige oth Erscheint auch als Online-Ausgabe 978-1-4419-7236-1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022458837&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ferrario, Davide L. Simplicial structures in topology Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4120861-4 |
| title | Simplicial structures in topology |
| title_alt | Strutture simpliciali in tolopogia |
| title_auth | Simplicial structures in topology |
| title_exact_search | Simplicial structures in topology |
| title_full | Simplicial structures in topology Davide L. Ferrario ; Renzo A. Piccinini |
| title_fullStr | Simplicial structures in topology Davide L. Ferrario ; Renzo A. Piccinini |
| title_full_unstemmed | Simplicial structures in topology Davide L. Ferrario ; Renzo A. Piccinini |
| title_short | Simplicial structures in topology |
| title_sort | simplicial structures in topology |
| topic | Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Algebraische Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022458837&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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