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Hodge theory for
intersection space cohomology
Markus Banagl and Eugénie Hunsicker |
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Geometry & Topology 23 (2019) 2165–2225
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Abstract |
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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 Poincaré 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 harmonic forms on the regular part, equipped with a fibred scattering metric. Some consequences of our methods for the signature are discussed as well. |
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Keywords
conifold transition, fibred cusp metrics, harmonic forms,
Hodge theorem, intersection cohomology, intersection form,
intersection space, $L^2$ cohomology, perversity function,
Poincaré duality, pseudomanifolds, scattering metrics,
signature theorem, stratified space
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Mathematical Subject Classification 2010
Primary: 55N33, 58A14
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References |
Publication
Received: 20 February 2015
Revised: 4 August 2017
Accepted: 11 October 2018
Published: 13 October 2019
Proposed: Steve Ferry
Seconded: Frances Kirwan, Ralph Cohen
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Authors |
| Markus Banagl | |
| Mathematisches Institut Universität Heidelberg Heidelberg Germany |
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| http://www.mathi.uni-heidelberg.de/~banagl/ | |
| Eugénie Hunsicker | |
| Department of Mathematical
Sciences Loughborough University Loughborough United Kingdom |
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| https://www.lboro.ac.uk/departments/maths/staff/academic/eug\% c3\% a9nie-hunsicker/ | |
