Configuration-like spaces and coincidences of maps on orbits

Details Configuration-like spaces and coincidences of maps on orbits Configuration-like spaces and coincidences of maps on orbits

2009-11-23

arxiv.org/abs/0911.4338v3

Algebraic & Geometric Topology, 11, 2011, 1033-1052

Mathematics

Algebraic Topology

Scientific paper

10.2140/agt.2011.11.1033

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.

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