Mathematics

Abstract: I will discuss a recently submitted paper, in which I prove the following theorem, concerning the space of positive scalar curvature metrics R⁺(X), on a smooth manifold X.

Theorem: Let X and Y be smooth manifolds, obtainable from each other via surgery in codimension at least three. Then the spaces R⁺(X) and R⁺(Y) are homotopy equivalent.

As a corollary I will demonstrate that in the case of spin manifolds of dimension at least five, the homotopy type of R⁺(X) is a spin-cobordism invariant.