Lectures on algebraic topology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Zürich
European Math. Soc.
2006
|
| Series: | EMS series of lectures in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | 99 S. graph. Darst. |
| ISBN: | 9783037190234 303719023X |
Staff View
MARC
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| 264 | 1 | |a Zürich |b European Math. Soc. |c 2006 | |
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Record in the Search Index
| _version_ | 1804135619562045440 |
|---|---|
| adam_text | Contents
Preface
.
v
1 Elements
of homology theory
]
1.1
Categories and functors
......................... 1
1.2
Some geometric properties of R^
................... 4
1.3
Chain complexes
............................ 7
1.4
Homology groups of a simplicial complex
............... 10
1.5
Simplicial maps
............................. 13
1.6
Induced homomorphisms of homology groups
............. 17
1.7
Degrees of maps between manifolds
.................. 18
1.8
Applications of the degree of a map
.................. 23
1.9
Relative homology
........................... 32
1.10
The exact homology sequence
..................... 33
1.11
Axiomatic point of view on homology
................. 37
1.12
Digression to the theory of Abelian groups
............... 39
1.13
Calculation of homology groups
.................... 41
1.14
Cellular homology
........................... 43
1.15
Lefschetz fixed point theorem
..................... 47
1.16
Homology with coefficients
....................... 50
1.17
Elements of cohomology theory
.................... 53
1.18
The
Poincaré
duality
.......................... 58
2
Elements of homotopy theory
61
2.1
Definition of the fundamental group
.................. 61
2.2
Independence of the choice of the base point
.............. 63
2.3
Presentations of groups
......................... 65
2.4
Calculation of fundamental groups
................... 68
2.5
Wirtinger s presentation
......................... 72
2.6
The higher homotopy groups
...................... 74
2.7
Bundles and exact sequences
...................... 76
2.8
Coverings
................................ 79
Answers, hints, solutions
........................... 83
Bibliography
................................. 95
Index
..................................... 97
|
| adam_txt |
Contents
Preface
.
v
1 Elements
of homology theory
]
1.1
Categories and functors
. 1
1.2
Some geometric properties of R^
. 4
1.3
Chain complexes
. 7
1.4
Homology groups of a simplicial complex
. 10
1.5
Simplicial maps
. 13
1.6
Induced homomorphisms of homology groups
. 17
1.7
Degrees of maps between manifolds
. 18
1.8
Applications of the degree of a map
. 23
1.9
Relative homology
. 32
1.10
The exact homology sequence
. 33
1.11
Axiomatic point of view on homology
. 37
1.12
Digression to the theory of Abelian groups
. 39
1.13
Calculation of homology groups
. 41
1.14
Cellular homology
. 43
1.15
Lefschetz fixed point theorem
. 47
1.16
Homology with coefficients
. 50
1.17
Elements of cohomology theory
. 53
1.18
The
Poincaré
duality
. 58
2
Elements of homotopy theory
61
2.1
Definition of the fundamental group
. 61
2.2
Independence of the choice of the base point
. 63
2.3
Presentations of groups
. 65
2.4
Calculation of fundamental groups
. 68
2.5
Wirtinger's presentation
. 72
2.6
The higher homotopy groups
. 74
2.7
Bundles and exact sequences
. 76
2.8
Coverings
. 79
Answers, hints, solutions
. 83
Bibliography
. 95
Index
. 97 |
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| ctrlnum | (OCoLC)70619273 (DE-599)BVBBV021758468 |
| dewey-full | 514.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.2 |
| dewey-search | 514.2 |
| dewey-sort | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T15:34:20Z |
| indexdate | 2024-07-09T20:43:23Z |
| institution | BVB |
| isbn | 9783037190234 303719023X |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014971597 |
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| physical | 99 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | European Math. Soc. |
| record_format | marc |
| series2 | EMS series of lectures in mathematics |
| spelling | Matveev, Sergej V. 1947- Verfasser (DE-588)124843956 aut Lekcii po algebraičeskoj topologii Lectures on algebraic topology Sergey V. Matveev Zürich European Math. Soc. 2006 99 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier EMS series of lectures in mathematics Aus d. Russ. übers. Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 s DE-604 Erscheint auch als ebook Matveev, Sergej V. Lectures on algebraic topology 978-3-03719-523-9 (DE-604)BV036706015 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014971597&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Matveev, Sergej V. 1947- Lectures on algebraic topology Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4120861-4 |
| title | Lectures on algebraic topology |
| title_alt | Lekcii po algebraičeskoj topologii |
| title_auth | Lectures on algebraic topology |
| title_exact_search | Lectures on algebraic topology |
| title_exact_search_txtP | Lectures on algebraic topology |
| title_full | Lectures on algebraic topology Sergey V. Matveev |
| title_fullStr | Lectures on algebraic topology Sergey V. Matveev |
| title_full_unstemmed | Lectures on algebraic topology Sergey V. Matveev |
| title_short | Lectures on algebraic topology |
| title_sort | lectures on algebraic topology |
| topic | Algebraic topology Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Algebraic topology Algebraische Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014971597&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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