The topology of infinite dimensional spaces and nonlinear proper Fredholm mappings

Abstract: In this talk I will discuss the differential topology of non-linear proper Fredholm mappings. In applications these mappings arise as non-linear PDE problems (of elliptic type). I will discuss work with Lauran Toussaint that relates these mappings to the stable homotopy groups of spheres, and if time permits, I will discuss an ongoing project on defining a new homology theory of singular type for infinite dimensional spaces. This is joint work with Alberto Abbondandolo, Michael Jung and Lauran Toussaint.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

Topology and Geometry Seminar (Texas, Kansas)