2134/17163
Eugenie Hunsicker
Eugenie
Hunsicker
Rafe Mazzeo
Rafe
Mazzeo
Harmonic forms on manifolds with edges
Loughborough University
2015
untagged
Mathematical Sciences not elsewhere classified
2015-03-31 10:15:47
Journal contribution
https://repository.lboro.ac.uk/articles/journal_contribution/Harmonic_forms_on_manifolds_with_edges/9386426
Let (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.