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Hodge theory for intersection space cohomology
journal contribution
posted on 2018-11-26, 10:03 authored by Markus Banagl, Eugenie HunsickerGiven 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.
Funding
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.
History
School
- Science
Department
- Mathematical Sciences
Published in
Geometry & TopologyVolume
23Issue
5Pages
2165 – 2225Citation
BANAGL, M. and HUNSICKER, E., 2018. Hodge theory for intersection space cohomology. Geometry & Topology, 23 (5), pp. 2165–2225.Publisher
Mathematical Sciences PublishersVersion
- VoR (Version of Record)
Rights holder
© Mathematical Sciences PublishersPublisher statement
First published in Geometry & Topology in Vol. 23 (2018), No. 5, published by Mathematical Sciences Publishers.Acceptance date
2018-10-11Publication date
2019-10-13Copyright date
2019ISSN
1465-3060eISSN
1364-0380Publisher version
Language
- en