文章基本信息

标题：On Expansion and Topological Overlap
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作者：Dominic Dotterrer ; Tali Kaufman ; Uli Wagner 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2016
卷号：51
页码：35:1-35:10
DOI：10.4230/LIPIcs.SoCG.2016.35
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We give a detailed and easily accessible proof of Gromov's Topological Overlap Theorem. Let X be a finite simplicial complex or, more generally, a finite polyhedral cell complex of dimension d. Informally, the theorem states that if X has sufficiently strong higher-dimensional expansion properties (which generalize edge expansion of graphs and are defined in terms of cellular cochains of X) then X has the following topological overlap property: for every continuous map X -> R^d there exists a point p in R^d whose preimage intersects a positive fraction mu > 0 of the d-cells of X. More generally, the conclusion holds if R^d is replaced by any d-dimensional piecewise-linear (PL) manifold M, with a constant \mu that depends only on d and on the expansion properties of X, but not on M.
关键词：Combinatorial Topology; Selection Lemmas; Higher-Dimensional Expanders