"The Topological Tverberg Conjecture"

Benjamin Braun
University of Kentucky

Monday, September 24, 2007
4:00 pm, 113 Patterson Office Tower

Abstract:

The Topological Tverberg Conjecture is as follows: Given integers n and d, set N=(d+1)(n-1); for every continuous map f from the N-simplex to d-dimensional Euclidean space, there exist n disjoint faces of the simplex whose images intersect under f. This conjecture is one of the most challenging open problems in topological combinatorics and is known to be valid when n is a prime power. We will sketch a proof of this for the case when n is prime and discuss some of the trouble one runs into when attempting the non-prime-power cases. The proof method we will discuss involves generalized Borsuk-Ulam theorems and numerical index theory, which we will develop from scratch.