Seminar of Algebraic and Differential Topology (Ismar Volić)
Monday 14.1.2019 at 10:30, Lecture room M/116
By: Differential Topology
Ismar Volić (Wellesley College):
Manifold calculus of functors for r-immersions
Manifold calculus of functors has in recent years been applied with great success to various spaces of embeddings, including spaces of knots and links. One can also apply this theory to spaces of r-immersions, which are immersions where no more than r-1 points are allowed to equal; embeddings are thus 2-immersions. In this talk, I will give some background on calculus of functors and then present some recent work on how this theory applies to r-immersions. More precisely, I will discuss the issue of the convergence of the Taylor tower that “approximates” this space. It turns out that manifold calculus in this context supplies interesting connections to combinatorial topology, such as the structure of certain subspace arrangements as well as Tverberg-like problems, so some time will be devoted to these topics. This is joint work with Franjo Šarčević.