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Extended Hodge theory for fibred cusp manifolds
journal contribution
posted on 2016-12-19, 14:26 authored by Eugenie HunsickerFor 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 AnalysisCitation
HUNSICKER, E., 2018. Extended Hodge theory for fibred cusp manifolds. Journal of Topology and Analysis, 10(03), pp. 531-562.Publisher
World Scientific PublishingVersion
- 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
2016-12-05Publication date
2018Notes
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/S1793525318500188ISSN
1793-5253eISSN
1793-7167Publisher version
Language
- en