Online seminar, U. Haifa Topology & Geometry seminar on March 7, 2021
A recording of the talk is available here:
Topology & Geometry Seminar
Speaker: Florian Frick, Carnegie Mellon University
Topic: The topological Tverberg problem beyond prime powers
Place: This is an online seminar. Please email David Blanc “blanc at math dot haifa dot ac dot il” for the Zoom ID and password.
Date: Sunday, March 7, 2021
Given d and q the topological Tverberg problem asks for the minimal n such that any continuous map from the n-dimensional simplex to R^d identifies q points from pairwise disjoint faces. For q a prime power n is (q-1)(d+1). The lower bound follows from a general position argument, the upper bound from equivariant topological methods. It was shown recently that for q with at least two distinct prime divisors the lower bound may be improved. For those q, non-trivial upper bounds had been elusive. I will show that n is at most q(d+1)-1 for all q. I had previously conjectured this to be optimal unless q is a prime power. This is joint work with Pablo Soberón.