Pollicott-Ruelle spectrum and Witten Laplacians (Q2031681)

In this paper, the asymptotic behavior of eigenvalues and eigenmodes of the Witten Laplacian on a smooth compact Riemannian manifold without boundary is studied. They converge to the Pollicott-Ruelle spectral data of the corresponding gradient flow acting on appropriate anisotropic Sobolev spaces. As an application, a natural family of quasimodes on the Witten deformation of the wedge product is studied, which satisf the Witten-Helffer-Sjostrand tunneling formulas and the Fukaya conjecture.