Hodge cohomology of some foliated boundary and foliated cusp metrics |
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| Authors: | Jesse Gell‐Redman Frédéric Rochon |
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| Affiliation: | 1. Department of Mathematics, University of Toronto, Toronto, ON, Canada;2. Département de Mathématiques, UQAM, Montréal (Québec), Canada |
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| Abstract: | For fibred boundary and fibred cusp metrics, Hausel, Hunsicker, and Mazzeo identified the space of L2 harmonic forms of fixed degree with the images of maps between intersection cohomology groups of an associated stratified space obtained by collapsing the fibres of the fibration at infinity onto its base. In the present paper, we obtain a generalization of this result to situations where, rather than a fibration at infinity, there is a Riemannian foliation with compact leaves admitting a resolution by a fibration. If the associated stratified space (obtained now by collapsing the leaves of the foliation) is a Witt space and if the metric considered is a foliated cusp metric, then no such resolution is required. |
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| Keywords: | Hodge theory L2‐cohomology microlocal analysis stratified spaces instantons 58J10 53C12 |
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