Configuration-like spaces and coincidences of maps on orbits

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.