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Extended Hodge theory for fibred cusp manifolds

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journal contribution
posted on 19.12.2016, 14:26 by Eugenie Hunsicker
For a particular class of pseudo manifolds, we show that the intersection cohomology groups for any perversity may be naturally represented by extended weighted L2 harmonic forms for a complete metric on the regular stratum with respect to some weight determined by the perversity. Extended weighted L2 harmonic forms are harmonic forms that are almost in the given weighted L2 space for the metric in question, but not quite. This result is akin to the representation of absolute and relative cohomology groups for a manifold with boundary by extended harmonic forms on the associated manifold with cylindrical ends. In analogy with that setting, in the unweighted L2 case, the boundary values of the extended harmonic forms de ne a Lagrangian splitting of the boundary space in the long exact sequence relating upper and lower middle perversity intersection cohomology groups.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Topology and Analysis

Citation

HUNSICKER, E., 2018. Extended Hodge theory for fibred cusp manifolds. Journal of Topology and Analysis, 10(03), pp. 531-562.

Publisher

World Scientific Publishing

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

05/12/2016

Publication date

2018

Notes

Electronic version of an article published as [Journal of Topology and Analysis, Volume, Issue, Year, Pages] 10.1142/S1793525318500188 © [copyright World Scientific Publishing Company] http://dx.doi.org/10.1142/S1793525318500188

ISSN

1793-5253

eISSN

1793-7167

Language

en

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