Functions on manifolds: algebraic and topological ascpects
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
1993
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| Series: | Translations of Mathematical Monographs
131 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russischen übersetzt |
| Physical Description: | X, 193 Seiten |
| ISBN: | 0821845780 |
Staff View
MARC
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| 240 | 1 | 0 | |a Funkcii na mnogoobrazijach |
| 245 | 1 | 0 | |a Functions on manifolds |b algebraic and topological ascpects |c V. V. Sharko |
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Record in the Search Index
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| adam_text | Contents
Preface ix
Chapter I. Frechet Manifolds 1
§ 1. Brief summary 1
§2. The Nash Moser Sergereart Hamilton category 10
§3. Stratification of smooth functions on a manifold 13
Chapter II. Minimal Morse Functions on Simply Connected
Manifolds 19
§1. Ordered minimal functions 19
§2. Equivalent epimorphisms 28
§3. Homotopy equivalent functions 33
§4. The realization theorem 38
§5. Isotopic functions 42
Chapter III. Stable Algebra 49
§ 1. Numerical invariants of modules 49
§2. Stably free modules 51
§3. Stable rank of a ring and additivity of fi(M) 53
§4. Thickening of epimorphisms 55
§5. Minimal epimorphisms and / rank(iV, M) 57
§6. Minimal resolutions 60
§7. n fold extensions of modules 62
Chapter IV. Homotopy of Chain Complexes 67
§1. Brief review 67
§2. Stable invariants of chain complexes 71
§3. The Whitehead group 76
§4. Torsion of homotopy equivalence 80
§5. Minimal complexes 83
§6. Morse numbers of complexes 91
Chapter V. Morse Numbers and Minimal Morse Functions 97
§ 1. Numerical invariants 98
§2. Morse numbers 102
vii
viii CONTENTS
§3. Minimal Morse functions on cobordisms 103
§4. Minimal Morse functions on cobordisms of class R 108
Chapter VI. Elements of the Homotopy Theory of
Non Simply Connected CW Complexes 113
§1. Brief review 113
§2. Torsion and simple homotopy type 116
§3. Two dimensional complexes 121
§4. Crossed modules 129
§5. Homotopy systems 135
§6. Homotopy type and stable isomorphism 141
§7. Minimal homotopy systems 144
§8. Minimal homotopy systems in a fixed homotopy type 147
Chapter VII. Minimal Morse Functions on Non Simply Connected
Manifolds 155
§1. Homotopy systems and Morse functions 155
§2. Minimal Morse functions on manifolds of class S 158
§3. A sufficient condition for the existence of a minimal Morse
function on a manifold of class S with a fixed fundamental
group 162
§4. Fundamental group and Morse numbers 164
§5. Minimal Morse functions on closed manifolds 165
Chapter VIII. Minimal Round Morse Functions 173
§1. Brief review 173
§2. Diagrams 178
§3. Minimal round Morse functions 184
Bibliography 187
|
| any_adam_object | 1 |
| author | Šarko, Vladimir V. |
| author_facet | Šarko, Vladimir V. |
| author_role | aut |
| author_sort | Šarko, Vladimir V. |
| author_variant | v v š vv vvš |
| building | Verbundindex |
| bvnumber | BV008931107 |
| classification_rvk | SK 350 |
| ctrlnum | (OCoLC)246828708 (DE-599)BVBBV008931107 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV008931107 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:26:56Z |
| institution | BVB |
| isbn | 0821845780 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005889621 |
| oclc_num | 246828708 |
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| owner_facet | DE-12 DE-188 |
| physical | X, 193 Seiten |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Translations of Mathematical Monographs |
| series2 | Translations of Mathematical Monographs |
| spelling | Šarko, Vladimir V. Verfasser aut Funkcii na mnogoobrazijach Functions on manifolds algebraic and topological ascpects V. V. Sharko Providence, RI American Mathematical Society 1993 X, 193 Seiten txt rdacontent n rdamedia nc rdacarrier Translations of Mathematical Monographs 131 Aus dem Russischen übersetzt Differenzierbare Abbildung (DE-588)4149802-1 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Glatte Mannigfaltigkeit (DE-588)4157471-0 gnd rswk-swf Morse-Theorie (DE-588)4197103-6 gnd rswk-swf Glatte Mannigfaltigkeit (DE-588)4157471-0 s Singularität Mathematik (DE-588)4077459-4 s Morse-Theorie (DE-588)4197103-6 s DE-604 Differenzierbare Abbildung (DE-588)4149802-1 s Translations of Mathematical Monographs 131 (DE-604)BV000002394 131 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005889621&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Šarko, Vladimir V. Functions on manifolds algebraic and topological ascpects Translations of Mathematical Monographs Differenzierbare Abbildung (DE-588)4149802-1 gnd Singularität Mathematik (DE-588)4077459-4 gnd Glatte Mannigfaltigkeit (DE-588)4157471-0 gnd Morse-Theorie (DE-588)4197103-6 gnd |
| subject_GND | (DE-588)4149802-1 (DE-588)4077459-4 (DE-588)4157471-0 (DE-588)4197103-6 |
| title | Functions on manifolds algebraic and topological ascpects |
| title_alt | Funkcii na mnogoobrazijach |
| title_auth | Functions on manifolds algebraic and topological ascpects |
| title_exact_search | Functions on manifolds algebraic and topological ascpects |
| title_full | Functions on manifolds algebraic and topological ascpects V. V. Sharko |
| title_fullStr | Functions on manifolds algebraic and topological ascpects V. V. Sharko |
| title_full_unstemmed | Functions on manifolds algebraic and topological ascpects V. V. Sharko |
| title_short | Functions on manifolds |
| title_sort | functions on manifolds algebraic and topological ascpects |
| title_sub | algebraic and topological ascpects |
| topic | Differenzierbare Abbildung (DE-588)4149802-1 gnd Singularität Mathematik (DE-588)4077459-4 gnd Glatte Mannigfaltigkeit (DE-588)4157471-0 gnd Morse-Theorie (DE-588)4197103-6 gnd |
| topic_facet | Differenzierbare Abbildung Singularität Mathematik Glatte Mannigfaltigkeit Morse-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005889621&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT sarkovladimirv funkciinamnogoobrazijach AT sarkovladimirv functionsonmanifoldsalgebraicandtopologicalascpects |