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Download fileHarmonic forms on manifolds with edges
journal contribution
posted on 31.03.2015, 10:15 authored by Eugenie Hunsicker, Rafe MazzeoLet (X, g) be a compact Riemannian stratified space with simple edge singularity.
Thus a neighbourhood of the singular stratum is a bundle of truncated cones over a
lower dimensional compact smooth manifold. We calculate the various polynomially
weighted de Rham cohomology spaces of X, as well as the associated spaces of
harmonic forms. In the unweighted case, this is closely related to recent work of
Cheeger and Dai [5]. Because the metric g is incomplete, this requires a consideration
of the various choices of ideal boundary conditions at the singular set. We also
calculate the space of L2 harmonic forms for any complete edge metric on the regular
part of X.
Funding
The first author was partially supported by the NSF through an ROA supplement to Grant DMS- 0204730. The second author was supported by the NSF through Grant DMS-0204730.
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