Event

Talk
Intersection Spaces, Fibered Scattering Metrics and Hodge Theory
9 Feb 2015, 14:30 – 15:30

We will start by describing a general homotopy theoretic method that associates to certain singular spaces geometric Poincaré complexes, the so-called intersection spaces. These depend on a perversity, just like Goresky-MacPherson's intersection cohomology, however, the cohomology of intersection spaces turns out to be quite different from intersection cohomology. We will provide motivation and some applications of this approach. Cheeger's Hodge theorem describes intersection cohomology by L2 harmonic forms. In the same spirit, in joint work with Eugenie Hunsicker, we describe the cohomology of intersection spaces by extended weighted L2 harmonic forms with respect to fibered scattering metrics, at least when the neighborhood of the singular stratum can be given a global product structure.