An \(L^{2}\) theory for differential forms on path spaces. I (Q2469820)

In this long paper, the authors construct a self-adjoint Hodge Laplacian on spaces of one- and two-forms over the manifold of continuous paths on a compact Riemannian manifold. The measure used is the Brownian motion measure or Wiener measure. The \(q\)-vectors 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 the path space plays an important role, and is also simply described. Malliavin calculus is a basic tool to derive these results.