A Homotopy-Theoretic Approach to the Topological Tverberg Conjecture

Let r≥2 and d≥1 be integers, let N=(d+1)(r-1), and let ΔN denote a standard N-simplex. The Topological Tverberg Conjecture states that any continuous map f: ΔN --\u3e Rd has r-fold self-intersections such that the preimages of the r-fold intersection points come from pairwise disjoint faces in the original simplex. F. Frick recently announced a counterexample to the conjecture for d≥ 3r+1, when r is not a power of a prime. This thesis will discuss an alternative analysis of Frick\u27s counterexample using the manifold calculus of functors. We hope that this technique will provide insight into other counterexamples to the Topological Tverberg Conjecture