gt-v23-n5-p01-s.pdf (604.55 kB)
0/0

Hodge theory for intersection space cohomology

Download (604.55 kB)
journal contribution
posted on 26.11.2018 by Markus Banagl, Eugenie Hunsicker
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.

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 & Topology

Volume

23

Issue

5

Pages

2165 – 2225

Citation

BANAGL, M. and HUNSICKER, E., 2018. Hodge theory for intersection space cohomology. Geometry & Topology, 23 (5), pp. 2165–2225.

Publisher

Mathematical Sciences Publishers

Version

VoR (Version of Record)

Rights holder

© Mathematical Sciences Publishers

Publisher statement

First published in Geometry & Topology in Vol. 23 (2018), No. 5, published by Mathematical Sciences Publishers.

Acceptance date

11/10/2018

Publication date

2019-10-13

Copyright date

2019

ISSN

1465-3060

eISSN

1364-0380

Language

en

Exports