Volume 11, issue 2 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Configuration-like spaces and coincidences of maps on orbits

R N Karasev and A Yu Volovikov

Algebraic & Geometric Topology 11 (2011) 1033–1052
Abstract

In this paper we study the spaces of q–tuples of points in a Euclidean space, without k–wise coincidences (configuration-like spaces). A transitive group action by permuting these points is considered, and some new upper bounds on the genus (in the sense of Krasnosel’skii–Schwarz and Clapp–Puppe) for this action are given. Some theorems of Cohen–Lusk type for coincidence points of continuous maps to Euclidean spaces are deduced.

Keywords
configuration space, coincidence, equivariant topology, Krasnosel'skii–Schwarz genus
Mathematical Subject Classification 2000
Primary: 55R80
Secondary: 55M20, 55M30, 55M35, 57S17
References
Publication
Received: 30 September 2009
Revised: 4 September 2010
Accepted: 5 October 2010
Published: 30 March 2011
Authors
R N Karasev
Department of Mathematics
Moscow Institute of Physics and Technology
Institutskiy per. 9
Dolgoprudny
Russia 141700
http://www.rkarasev.ru/en/
A Yu Volovikov
Department of Mathematics
University of Texas at Brownsville
80 Fort Brown
Brownsville TX 78520
USA
Department of Higher Mathematics
Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
Pr. Vernadskogo 78
Moscow 117454
Russia