Equivariant maps from a configuration space to a sphere
Equivariant maps from a configuration space to a sphere

Günter Ziegler, Freie Universität, Berlin
Fine Hall 314
THIS IS A JOINT TOPOLOGY/ALGEBRAIC TOPOLOGY SEMINAR. There are several distinct reasons to ask for the existence of an S_nequivariant map from the configuration space F(R^d,n) of n labeled points in R^d to a certain S_nrepresentation sphere of dimension (d+1)(n1)1. We will describe some of these reasons and sketch several approaches towards such BorsukUlam type problems. We obtain a complete answer using equivariant obstruction theory, based on regular cell complex models for the configuration spaces, and a tiny dose of number theory. Joint work with P. V. M. Blagojevic and W. Lück.