A tight colored Tverberg theorem for maps to manifolds
type: Item
instance of: scholarly article
title: A tight colored Tverberg theorem for maps to manifolds
zbMATH Open document ID: 1232.55003
author: Pavle V. M. Blagojević
author: Benjamin Matschke
author: Günter M. Ziegler
published in: Topology and its Applications
publication date: 2011-08-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1107.1904
review text: A coloring of the vertices of a simplex \(\Delta\) is a partition of the vertex set into color classes. A face of \(\Delta\) is called a rainbow face if its vertices have different colors. The authors prove the following result: Let \(N = (d + 1)(r - 1)\), where \(d \geq 1\) and \(r \geq 2\) is a prime number. If \(M\) is a \(d\)-dimensional manifold and \(\Delta_N\) is an \(N\)-dimensional simplex whose vertices are colored such that all color classes are of size at most \(r - 1\) then for every continuous map \(f: \Delta_N \rightarrow M\) there exist \(r\) disjoint rainbow faces of \(\Delta_N\) whose images under \(f\) have a point in common.
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 52B70
Mathematics Subject Classification ID: 05D05
Mathematics Subject Classification ID: 52A35
zbMATH DE Number: 5935889
zbMATH Keywords: colored Tverberg problem
zbMATH Keywords: deleted product/join configuration space
zbMATH Keywords: equivariant cohomology
zbMATH Keywords: Fadell-Husseini index
zbMATH Keywords: Serre spectral sequence
reviewed by: Mircea Balaj
MaRDI profile type: Publication
OpenAlex ID: W2162312428
arXiv ID: 1107.1904
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DOI: 10.1016/J.TOPOL.2011.05.016
description: scientific article