Using the Borsuk–Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2003
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | "The "Kneser conjecture" -- posed by Martin Kneser in 1955 in the Jahresbericht der DMV -- is an innocent-looking problem about partitioning the k-subsets of an n-set into intersecting subfamilies. Its striking solution by L. Lovász featured an unexpected use of the Borsuk-Ulam theorem, that is, of a genuinely topological result about continuous antipodal maps of spheres. Matousek's lively little textbook now shows that Lovász' insight as well as beautiful work of many others (such as Vrecica and Zivaljevic, and Sarkaria) have opened up an exciting area of mathematics that connects combinatorics, graph theory, algebraic topology and discrete geometry. What seemed like an ingenious trick in 1978 now presents itself as an instance of the "test set paradigm": to construct configuration spaces for combinatorial problems such that coloring, incidence or transversal problems may be translated into the (non-)existence of suitable equivariant maps. The vivid account of this area and its ramifications by Matousek is an exciting, a coherent account of this area of topological combinatorics. It features a collection of mathematical gems written with a broad view of the subject and still with loving care for details. Recommended reading! […]" Günter M.Ziegler (Berlin) Zbl. MATH Volume 1060 Productions-no.: 05001 |
| Beschreibung: | 1 Online-Ressource (XII, 214 p) |
| ISBN: | 9783540766490 9783540003625 |
| DOI: | 10.1007/978-3-540-76649-0 |
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Datensatz im Suchindex
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| author | Matoušek, Jiří |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-540-76649-0 |
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| isbn | 9783540766490 9783540003625 |
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| spelling | Matoušek, Jiří Verfasser aut Using the Borsuk–Ulam Theorem Lectures on Topological Methods in Combinatorics and Geometry by Jiří Matoušek Berlin, Heidelberg Springer Berlin Heidelberg 2003 1 Online-Ressource (XII, 214 p) txt rdacontent c rdamedia cr rdacarrier Universitext "The "Kneser conjecture" -- posed by Martin Kneser in 1955 in the Jahresbericht der DMV -- is an innocent-looking problem about partitioning the k-subsets of an n-set into intersecting subfamilies. Its striking solution by L. Lovász featured an unexpected use of the Borsuk-Ulam theorem, that is, of a genuinely topological result about continuous antipodal maps of spheres. Matousek's lively little textbook now shows that Lovász' insight as well as beautiful work of many others (such as Vrecica and Zivaljevic, and Sarkaria) have opened up an exciting area of mathematics that connects combinatorics, graph theory, algebraic topology and discrete geometry. What seemed like an ingenious trick in 1978 now presents itself as an instance of the "test set paradigm": to construct configuration spaces for combinatorial problems such that coloring, incidence or transversal problems may be translated into the (non-)existence of suitable equivariant maps. The vivid account of this area and its ramifications by Matousek is an exciting, a coherent account of this area of topological combinatorics. It features a collection of mathematical gems written with a broad view of the subject and still with loving care for details. Recommended reading! […]" Günter M.Ziegler (Berlin) Zbl. MATH Volume 1060 Productions-no.: 05001 Mathematics Information theory Computational complexity Combinatorics Algebraic topology Algebraic Topology Discrete Mathematics in Computer Science Theory of Computation Mathematics, general Mathematik 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 1\p DE-604 https://doi.org/10.1007/978-3-540-76649-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Matoušek, Jiří Using the Borsuk–Ulam Theorem Lectures on Topological Methods in Combinatorics and Geometry Mathematics Information theory Computational complexity Combinatorics Algebraic topology Algebraic Topology Discrete Mathematics in Computer Science Theory of Computation Mathematics, general Mathematik 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 by Jiří Matoušek |
| title_fullStr | Using the Borsuk–Ulam Theorem Lectures on Topological Methods in Combinatorics and Geometry by Jiří Matoušek |
| title_full_unstemmed | Using the Borsuk–Ulam Theorem Lectures on Topological Methods in Combinatorics and Geometry by Jiří Matoušek |
| 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 | Mathematics Information theory Computational complexity Combinatorics Algebraic topology Algebraic Topology Discrete Mathematics in Computer Science Theory of Computation Mathematics, general Mathematik Kombinatorische Geometrie (DE-588)4140733-7 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Mathematics Information theory Computational complexity Combinatorics Algebraic topology Algebraic Topology Discrete Mathematics in Computer Science Theory of Computation Mathematics, general Mathematik Kombinatorische Geometrie Algebraische Topologie |
| url | https://doi.org/10.1007/978-3-540-76649-0 |
| work_keys_str_mv | AT matousekjiri usingtheborsukulamtheoremlecturesontopologicalmethodsincombinatoricsandgeometry |