On a topological generalization of the Tverberg theorem
type: Item
instance of: scholarly article
title: On a topological generalization of the Tverberg theorem
zbMATH Open document ID: 0879.55004
DOI: 10.1007/BF02308547
published in: Mathematical Notes
publication date: 1997-07-14T00:00:00Z
review text: Let \(\Delta^N\) denote an \(N\)-dimensional simplex and \(M^m\) an \(m\)-dimensional topological manifold. The main result. Let \(q=p^n\) where \(p\) is an arbitrary prime number, \(N=(q-1)(m+1)\) and \(f:\partial\Delta^N\to M^m\) be a continuous map. For \(q=2\) it is supposed additionally that the modulo 2 degree of the map \(f\) equals zero. Then there exist \(q\) mutually disjoint closed faces of \(\Delta^N\) such that the intersection of their \(f\)-images is nonempty.
Mathematics Subject Classification ID: 55M25
Mathematics Subject Classification ID: 57Q05
zbMATH DE Number: 1028528
zbMATH Keywords: topological degree
zbMATH Keywords: simplex
zbMATH Keywords: topological manifold
author: Alexey Volovikov
reviewed by: Valerii V. Obukhovskij
MaRDI profile type: Publication
cites work: On a common generalization of Borsuk's and Radon's theorem
cites work: On a Topological Generalization of a Theorem of Tverberg
cites work: A Generalization of Radon's Theorem
cites work: Q3866809
cites work: Nonsymmetric version of Bourgin-Yang theorem for multi-valued maps and free \(Z_ p\)-actions
description: scientific article; zbMATH DE number 1028528