Intersection cohomology, or IH*, is a topological tool defined in the 1980s to investigate a class of singular spaces called pseudo manifolds. Every point on a pseudo manifold, X, has a neighbourhood that looks like a disk cross the cone on a lower dimensional pseudo manifold called the link at that point. IH*(X) arises from a local upper truncation of the link cohomology. Several Hodge theorems have been proved relating IH(X) to harmonic forms for finite volume metrics on the regular part of X.
HI cohomology is a new cohomology theory for pseudo manifolds defined by M. Banagl based on the idea of co-truncation in the links, that is, using a lower truncation in the link cohomology. This talk will describe ongoing work relating this cohomology to harmonic forms for infinite volume metrics on the regular part of X.
(Joint work with M. Banagl)
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