Using the Borsuk-Ulam theorem: lectures on topological methods in combinatorics and geometry
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2003
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 173 - 187 |
| Physical Description: | XII, 196 S. graph. Darst. |
| ISBN: | 3540003622 |
Staff View
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Record in the Search Index
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| adam_text | JIRI MATOUSEK USING THE BORSUK-ULAM THEOREM LECTURES ON TOPOLOGICAL
METHODS IN COMBINATORICS AND GEOMETRY WRITTEN IN COOPERATION WITH ANDERS
BJORNER AND GUNTER M. ZIEGLER SPRINGER CONTENTS PREFACE V PRELIMINARIES
XI 1. SIMPLICIAL COMPLEXES 1 1.1 TOPOLOGICAL SPACES 1 1.2 HOMOTOPY
EQUIVALENCE AND HORAOTOPY 4 1.3 GEOMETRIC SIMPLICIAL COMPLEXES 7 1.4
TRIANGULATIONS 10 1.5 ABSTRACT SIMPLICIAL COMPLEXES 13 1.6 DIMENSION OF
GEOMETRIC REALIZATIONS 16 1.7 SIMPLICIAL COMPLEXES AND POSETS 17 2. THE
BORSUK-ULAM THEOREM 21 2.1 THE BORSUK-ULAM THEOREM IN VARIOUS GUISES 22
2.2 A GEOMETRIC PROOF 30 2.3 A DISCRETE VERSION: TUCKER S LEMMA 34 2.4
ANOTHER PROOF OF TUCKER S LEMMA 41 3. DIRECT APPLICATIONS OF BORSUK-ULAM
47 3.1 THE HAM SANDWICH THEOREM 47 3.2 ON MULTICOLORED PARTITIONS AND
NECKLACES 53 3.3 KNESER S CONJECTURE 57 3.4 MORE GENERAL KNESER GRAPHS:
DOL NIKOV S THEOREM 61 3.5 GALE S LEMMA AND SCHRIJVER S THEOREM 64 4. A
TOPOLOGICAL INTERLUDE 69 4.1 QUOTIENT SPACES 69 4.2 JOINS (AND PRODUCTS)
73 4.3 FC-CONNECTEDNESS 78 4.4 RECIPES FOR SHOWING FC-CONNECTEDNESS 80
4.5 CELL COMPLEXES 82 X CONTENTS 5. Z2-MAPS AND NONEMBEDDABILITY 87 5.1
NONEMBEDDABILITY THEOREMS: AN INTRODUCTION 88 5.2 Z 2 -SPACES AND Z 2
-MAPS 92 5.3 THE Z 2 -INDEX 95 5.4 DELETED PRODUCTS GOOD 103 5.5 ...
DELETED JOINS BETTER 107 5.6 BIER SPHERES AND THE VAN KAMPEN-FLORES
THEOREM ILL 5.7 SARKARIA S INEQUALITY 116 5.8 NONEMBEDDABILITY AND
KNESER COLORINGS 119 5.9 A GENERAL LOWER BOUND FOR THE CHROMATIC NUMBER
123 6. MULTIPLE POINTS OF COINCIDENCE 133 6.1 G-SPACES 133 6.2 E N G
SPACES AND THE G-INDEX 137 6.3 DELETED JOINS AND DELETED PRODUCTS 145
6.4 NECKLACE FOR MANY THIEVES 149 6.5 THE TOPOLOGICAL TVERBERG THEOREM
151 6.6 MANY TVERBERG PARTITIONS 155 6.7 ZP-INDEX, KNESER COLORINGS, AND
P-FOLD POINTS 157 6.8 THE COLORED TVERBERG THEOREM 161 A QUICK SUMMARY
165 HINTS TO SELECTED EXERCISES 171 REFERENCES 173 INDEX 189
|
| any_adam_object | 1 |
| author | Matoušek, Jiří 1963-2015 |
| author_GND | (DE-588)124638457 |
| author_facet | Matoušek, Jiří 1963-2015 |
| author_role | aut |
| author_sort | Matoušek, Jiří 1963-2015 |
| author_variant | j m jm |
| building | Verbundindex |
| bvnumber | BV017200676 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612 |
| callnumber-search | QA612 |
| callnumber-sort | QA 3612 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 300 |
| classification_tum | MAT 550f |
| ctrlnum | (OCoLC)248855144 (DE-599)BVBBV017200676 |
| 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 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV017200676 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:14:55Z |
| institution | BVB |
| isbn | 3540003622 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010365789 |
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| physical | XII, 196 S. graph. Darst. |
| publishDate | 2003 |
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| publisher | Springer |
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| series2 | Universitext |
| spelling | Matoušek, Jiří 1963-2015 Verfasser (DE-588)124638457 aut Using the Borsuk-Ulam theorem lectures on topological methods in combinatorics and geometry Jiří Matoušek. Written in cooperation with Anders Björner and Günter M. Ziegler Berlin [u.a.] Springer 2003 XII, 196 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Literaturverz. S. 173 - 187 Algebraïsche topologie gtt Analyse combinatoire Complexos simpliciais larpcal Géométrie combinatoire Géométrie combinatoire rasuqam Théorème de Borsuk-Ulam rasuqam Topologia algébrica larpcal Topologia larpcal Topologie algébrique Topologie algébrique rasuqam Algebraic topology Combinatorial analysis Combinatorial geometry Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Kombinatorische Geometrie (DE-588)4140733-7 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 s Kombinatorische Geometrie (DE-588)4140733-7 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010365789&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Matoušek, Jiří 1963-2015 Using the Borsuk-Ulam theorem lectures on topological methods in combinatorics and geometry Algebraïsche topologie gtt Analyse combinatoire Complexos simpliciais larpcal Géométrie combinatoire Géométrie combinatoire rasuqam Théorème de Borsuk-Ulam rasuqam Topologia algébrica larpcal Topologia larpcal Topologie algébrique Topologie algébrique rasuqam Algebraic topology Combinatorial analysis Combinatorial geometry Algebraische Topologie (DE-588)4120861-4 gnd Kombinatorische Geometrie (DE-588)4140733-7 gnd |
| subject_GND | (DE-588)4120861-4 (DE-588)4140733-7 |
| title | Using the Borsuk-Ulam theorem lectures on topological methods in combinatorics and geometry |
| title_auth | Using the Borsuk-Ulam theorem lectures on topological methods in combinatorics and geometry |
| title_exact_search | Using the Borsuk-Ulam theorem lectures on topological methods in combinatorics and geometry |
| title_full | Using the Borsuk-Ulam theorem lectures on topological methods in combinatorics and geometry Jiří Matoušek. Written in cooperation with Anders Björner and Günter M. Ziegler |
| title_fullStr | Using the Borsuk-Ulam theorem lectures on topological methods in combinatorics and geometry Jiří Matoušek. Written in cooperation with Anders Björner and Günter M. Ziegler |
| title_full_unstemmed | Using the Borsuk-Ulam theorem lectures on topological methods in combinatorics and geometry Jiří Matoušek. Written in cooperation with Anders Björner and Günter M. Ziegler |
| title_short | Using the Borsuk-Ulam theorem |
| title_sort | using the borsuk ulam theorem lectures on topological methods in combinatorics and geometry |
| title_sub | lectures on topological methods in combinatorics and geometry |
| topic | Algebraïsche topologie gtt Analyse combinatoire Complexos simpliciais larpcal Géométrie combinatoire Géométrie combinatoire rasuqam Théorème de Borsuk-Ulam rasuqam Topologia algébrica larpcal Topologia larpcal Topologie algébrique Topologie algébrique rasuqam Algebraic topology Combinatorial analysis Combinatorial geometry Algebraische Topologie (DE-588)4120861-4 gnd Kombinatorische Geometrie (DE-588)4140733-7 gnd |
| topic_facet | Algebraïsche topologie Analyse combinatoire Complexos simpliciais Géométrie combinatoire Théorème de Borsuk-Ulam Topologia algébrica Topologia Topologie algébrique Algebraic topology Combinatorial analysis Combinatorial geometry Algebraische Topologie Kombinatorische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010365789&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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