David Elworthy
An L2 differential form theory on path spaces.
A selfadjoint Hodge Laplacian is constructed on spaces of one and two forms over the manifold of continuous paths on a compact Riemannian manifold. The measure used is Brownian motion measure. The qvectors involved, dual to the forms, are perturbations of the usual exterior powers of"finite energy" tangent vectors by a curvature term. The "damped Markovian connection" on path space plays an important role, and will be simply described. A proposal for extending this to forms of all degrees will be given.
The talk is based on: "An L2 theory for differential forms on path spaces I", K. D. Elworthy & XueMei Li, available on http://www.xuemei.org/bib.html
