On kregular maps
On kregular maps

Pavle Blagojevic , Freie Universität, Berlin
Fine Hall 214
The question about the existence of a continuous kregular map from a topological space X to an Ndimensional Euclidean space R^N, which would map any k distinct points in X to linearly independent vectors in R^N, was first considered by Borsuk in 1957. In this talk we present a proof of the following theorem, which extends results by CohenHandel 1978 (for d=2) and Chisholm 1979 (for d power of 2): For integers k and d greater then zero, there is no kregular map R^d > R^N for N < d(ka(k))+a(k), where a(k) is the number of ones in the dyadic expansion of k. Joint work with G. M. Ziegler and W. Lück.