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Title: Extended Hodge theory for fibred cusp manifolds
Authors: Hunsicker, Eugenie
Issue Date: 2017
Publisher: World Scientific Publishing
Citation: HUNSICKER, E., 2017. Extended Hodge theory for fibred cusp manifolds. Journal of Topology and Analysis, [in press]
Abstract: 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.
Description: This paper is closed access until 10 February 2018.
Version: Accepted for publication
DOI: 10.1142/S1793525318500188
URI: https://dspace.lboro.ac.uk/2134/23527
Publisher Link: http://dx.doi.org/10.1142/S1793525318500188
ISSN: 1793-5253
Appears in Collections:Closed Access (Maths)

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