Introduction to algebraic topology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham
Birkhäuser
[2023]
|
| Edition: | corrected publication |
| Series: | Compact textbooks in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | viii, 182 Seiten Illustrationen, Diagramme |
| ISBN: | 9783030983123 |
Staff View
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Record in the Search Index
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| adam_text |
Contents 1 2 Basic Notions of Category Theory. 1.1 Categories . 1.2 Functors . 1.3 Natural Transformations. 1.4 Adjunction. 1.5 Limits and Colimits. Exercises. 1 1 4 6 9 11 29 Fundamental Groupoid and van Kämpen’s Theorem. 33 33 35 41 53 56 58 2.1 The Fundamental Groupoid. 2.2 Van Kampen’s Theorem. 2.3 Cofibrations and Homotopy Pushouts. 2.4 Computing Fundamental Groups. 2.5 Higher Homotopy Groups. Exercises. 3 Homology: Ideas and Axioms . 3.1 The Idea of
Homology. 3.2 Simplicial Homology. 3.3 Relative Simplicial Homology with Coefficients. 3.4 The Eilenberg-Steenrod Axioms for Homology. 3.5 Simplicial Approximation. Exercises. 4 Singular Homology. 4.1 The Definition of Singular Homology. 4.2 The Long Exact Sequence of a Pair of Spaces. 4.3 Homotopy Invariance. 4.4 Excision . 4.5 Singular Homology in Degree Zero and One. Exercises. 5 Homology: Computations and Applications. 5.1 Relative vs. Absolute Homology. 5.2 Simplicial and Singular Homology Agree. 5.3 The Mayer-Vietoris Sequence
. 59 59 61 66 71 73 77 79 79 81 84 88 96 100 103 103 110 114 vii
viii Contents 5.4 Degree. 120 5.5 Applications. 126 Exercises. 132 6 Cellular Homology. 6.1 CW Complexes. 6.2 Cellular Homology and Euler Characteristic. 6.3 Computing Cellular Homology . 6.4 Uniqueness of Ordinary Homology. 6.5 How to Proceed. Exercises. 135 135 146 155 160 164 167 Correction to: Introduction to Algebraic Topology. Cl A Quotient Topology. 169 Bibliography. 173 List of Notation. 175
Index. 179 |
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| id | DE-604.BV049736803 |
| illustrated | Illustrated |
| indexdate | 2024-11-11T09:07:44Z |
| institution | BVB |
| isbn | 9783030983123 |
| language | English |
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| owner | DE-573 DE-739 |
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| physical | viii, 182 Seiten Illustrationen, Diagramme |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Compact textbooks in mathematics |
| spelling | Kammeyer, Holger Verfasser (DE-588)1186398531 aut Introduction to algebraic topology Holger Kammeyer corrected publication Cham Birkhäuser [2023] viii, 182 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Compact textbooks in mathematics Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 s DE-604 Erscheint auch als Online-Ausgabe 978-3-030-98313-0 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035078871&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kammeyer, Holger Introduction to algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4120861-4 |
| title | Introduction to algebraic topology |
| title_auth | Introduction to algebraic topology |
| title_exact_search | Introduction to algebraic topology |
| title_full | Introduction to algebraic topology Holger Kammeyer |
| title_fullStr | Introduction to algebraic topology Holger Kammeyer |
| title_full_unstemmed | Introduction to algebraic topology Holger Kammeyer |
| title_short | Introduction to algebraic topology |
| title_sort | introduction to algebraic 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=035078871&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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