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
2008
|
| Edition: | corr. 2. print. |
| Series: | Universitext
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 173 - 187 |
| Physical Description: | XII, 210 S. graph. Darst. |
| ISBN: | 9783540003625 |
Staff View
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| 245 | 1 | 0 | |a Using the Borsuk-Ulam theorem |b lectures on topological methods in combinatorics and geometry |c Jiří Matoušek. Written in cooperation with Anders Björner and Günter M. Ziegler |
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Record in the Search Index
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|---|---|
| adam_text | Contents Preface................................................................................................................... v Preliminaries...................................................................................................... xi Simplicial Complexes............................................................................ 1.1 Topological Spaces......................................................................... 1.2 Homotopy Equivalence and Homotopy..................................... 1 1 4 7 10 13 16 17 1. 2. 3. 1.3 1.4 1.5 1.6 1.7 Geometric Simplicial Complexes................................................. Triangulations ............................................................................... Abstract Simplicial Complexes................................................... Dimension of Geometric Realizations......................................... Simplicial Complexes and Posets ............................................... The 2.1 2.2 2.3 2.4 Borsuk—Ulam Theorem .............................................................. The Borsuk-Ulam Theorem in Various Guises......................... Direct Applications of Borsuk—Ulam............................................. 3.1 3.2 3.3 3.4 3.5 4. A Geometric Proof....................................................................... A Discrete Version: Tucker’s Lemma......................................... Another Proof of Tucker’s Lemma............................................. The Ham Sandwich Theorem ..................................................... On Multicolored
Partitions and Necklaces ............................... Kneser’s Conjecture ..................................................................... More General Kneser Graphs: Dol’nikov’s Theorem............... Gale’s Lemma and Schrijver’s Theorem ................................... A Topological Interlude........................................................................ 4.1 Quotient Spaces............................................................................. 4.2 Joins (and Products)..................................................................... 4.3 ^-Connectedness ........................................................................... 4.4 Recipes for Showing ^-Connectedness....................................... 4.5 Gell Complexes ............................................................................. 21 22 30 35 42 47 47 53 57 61 64 69 69 73 78 80 82
x Contents 5. 2г-Марѕ and Nonembeddability.................................................. 87 5.1 Nonembeddability Theorems: An Introduction....................... 88 5.2 Z2-Spaces and Z2-Maps............................................................... 92 5.3 The Z2֊Index ............................................................................... 95 5.4 Deleted Products Good.................................................................. 108 5.5 ... Deleted Joins Better.................................................................. 112 5.6 Bier Spheres and the Van Kampen-Flores Theorem............... 116 5.7 Sarkaria’s Inequality........................................................................121 5.8 Nonembeddability and Kneser Colorings..................................... 124 5.9 A General Lower Bound for the ChromaticNumber.................128 6. Multiple Points of Coincidence ...................................................... 145 6.1 G֊Spaces........................................................................................... 145 6.2 EnG Spaces and the G-Index....................................................... 149 6.3 Deleted Joins and Deleted Products ........................................... 157 6.4 The Topological Tverberg Theorem............................................. 161 6.5 Many Tverberg Partitions............................................................. 165 6.6 Necklace for Many Thieves ........................................................... 167 6.7 Zp-Index, Kneser Colorings, and p-Fold
Points......................... 170 6.8 The Colored Tverberg Theorem................................................... 174 A Quick Summary........................................................................................ 179 Hints to Selected Exercises...................................................................... 185 References........................................................................................................ 187 Index..................................................................................................................203
|
| any_adam_object | 1 |
| author | Matoušek, Jiří 1963-2015 |
| author_GND | (DE-588)124638457 |
| author_facet | Matoušek, Jiří 1963-2015 |
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| author_sort | Matoušek, Jiří 1963-2015 |
| author_variant | j m jm |
| building | Verbundindex |
| bvnumber | BV042337390 |
| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 170 SK 300 |
| classification_tum | MAT 550f |
| ctrlnum | (OCoLC)254475833 (DE-599)BVBBV042337390 |
| 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 |
| edition | corr. 2. print. |
| format | Book |
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| id | DE-604.BV042337390 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:18:47Z |
| institution | BVB |
| isbn | 9783540003625 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027773990 |
| oclc_num | 254475833 |
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| owner_facet | DE-188 DE-29T DE-739 |
| physical | XII, 210 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| 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 corr. 2. print. Berlin [u.a.] Springer 2008 XII, 210 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 Kombinatorische Geometrie (DE-588)4140733-7 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 s Kombinatorische Geometrie (DE-588)4140733-7 s DE-604 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=027773990&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 Kombinatorische Geometrie (DE-588)4140733-7 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4140733-7 (DE-588)4120861-4 |
| 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 Kombinatorische Geometrie (DE-588)4140733-7 gnd Algebraische Topologie (DE-588)4120861-4 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 Kombinatorische Geometrie Algebraische Topologie |
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