Hodge theory for intersection space cohomology
journal contributionposted on 26.11.2018 by Markus Banagl, Eugenie Hunsicker
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Given a perversity function in the sense of intersection homology theory, the method of intersection spaces assigns to certain oriented stratified spaces cell complexes whose ordinary reduced homology with real coefficients satisfies Poincare duality across complementary perversities. The resulting homology theory is well-known not to be isomorphic to intersection homology. For a two-strata pseudomanifold with product link bundle, we give a description of the cohomology of intersection spaces as a space of weighted L2 harmonic forms on the regular part, equipped with a fibred scattering metric. Some consequences of our methods for the signature are discussed as well.
The first author was in part supported by a research grant of the Deutsche Forschungsgemeinschaft. The authors thank the Deutsche Forschungsgemeinschaft and the London Mathematical Society for funding the research visits during which much of this work was done.
- Mathematical Sciences