Volume 12, issue 4 (2012)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Bourgin–Yang version of the Borsuk–Ulam theorem for $\mathbb{Z}_{p^k}$–equivariant maps

Wacław Marzantowicz, Denise de Mattos and Edivaldo L dos Santos

Algebraic & Geometric Topology 12 (2012) 2245–2258
Abstract

Let G = pk be a cyclic group of prime power order and let V and W be orthogonal representations of G with V G = WG = {0}. Let S(V ) be the sphere of V and suppose f : S(V ) W is a G–equivariant mapping. We give an estimate for the dimension of the set f1{0} in terms of V and W. This extends the Bourgin–Yang version of the Borsuk–Ulam theorem to this class of groups. Using this estimate, we also estimate the size of the G–coincidences set of a continuous map from S(V ) into a real vector space W.

Keywords
equivariant maps, covering dimension, orthogonal representation, equivariant $K$–theory
Mathematical Subject Classification 2010
Primary: 55M20
Secondary: 55M35, 55N91, 57S17
References
Publication
Received: 30 April 2012
Revised: 14 August 2012
Accepted: 27 August 2012
Published: 5 January 2013
Authors
Wacław Marzantowicz
Faculty of Mathematics and Computer Science
Adam Mickiewicz University of Poznań
ul. Umultowska 87
61-614 Poznań
Poland
Denise de Mattos
Instituto de Ciências Matemáticas e de Computação
Departamento de Matemática
Universidade de São Paulo
Caixa Postal 668
13560-970 São Carlos
Brazil
http://www.icmc.usp.br/~topologia/
Edivaldo L dos Santos
Departamento de Matemática
Universidade Federal de São Carlos
Caixa Postal 676
13565-905 São Carlos
Brazil
http://www2.dm.ufscar.br/~edivaldo/