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.

References in corpus (4)

• On the category of Euclidean configuration spaces and associated fibrations
• The genus and the category of configuration spaces
• Periodic billiard trajectories in smooth convex bodies
• Knaster's problem for almost $(Z_p{)}^k$-orbits