An index formula for the intersection {Euler} characteristic of an infinite cone

Ludwig, Ursula

Abstract

The aim of this article is to establish an index formula for the intersection Euler characteristic of a cone. The main actor is the model Witten Laplacian on the infinite cone. First, we study its spectral properties and establish a McKean-Singer type formula. We also give an explicit formula for the zeta function of the model Witten Laplacian. In a second step, we apply local index techniques to the model Witten Laplacian. By combining these two steps, we express the absolute and relative intersection Euler characteristic of the cone as a sum of two terms, a term which is local, and a second term which is the Cheeger invariant.