A Borsuk--Ulam theorem for \((\mathbb Z_p)^k\)-actions on products of \((\text{mod}\,p)\) homology spheres
type: Item
instance of: scholarly article
title: A Borsuk--Ulam theorem for \((\mathbb Z_p)^k\)-actions on products of \((\text{mod}\,p)\) homology spheres
zbMATH Open document ID: 1120.55003
author: Yuri A. Turygin
published in: Topology and its Applications
publication date: 2007-02-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0510086
review text: Let \(p\) be a prime number and \(f:N^{n_1}\times\dots\times N^{n_k}\to \mathbb R^m\) be a continuous map defined on the product of (mod\,\(p\)) homology \(n_i\)-spheres \(N^{n_i}\) where \(n_i\) is odd if \(p\) is odd. It is proved that for the product of free actions of \(\mathbb Z_p\) on the spaces \(N^{n_i}\) the coincidence set \(A(f)=\{x\in N^{n_1}\times\dots\times N^{n_k}:\forall g\in (\mathbb Z_p)^k\;\;f(x)=f(gx)\}\) has dimension at least \(n_1+\dots+ n_k-m(p^k-1)\), provided \(n_i\geq m p^{i-1}(p-1)\) for all \(i\leq k\).
reviewed by: Taras Banakh
Mathematics Subject Classification ID: 55M35
Mathematics Subject Classification ID: 55M10
Mathematics Subject Classification ID: 57S17
zbMATH DE Number: 5123630
zbMATH Keywords: vector bundle
zbMATH Keywords: Euler class
zbMATH Keywords: Chern classes
zbMATH Keywords: Stiefel-Whitney classes
MaRDI profile type: Publication
OpenAlex ID: W2600881195
arXiv ID: math/0510086
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DOI: 10.1016/J.TOPOL.2006.06.004
description: scientific article