Witten deformation and the spectral package of a Riemannian manifold

Abstract

The Witten deformation associated to a Morse function on a closed Riemannian manifold, via Rellich-Kato theorem, relates analytically the spectral package of the Riemannian manifold (eigenvalues and eigenforms) to the Morse complex defined by the pair (Morse function, Riemannian metric) coupled with the "multivariable harmonic oscillators" associated to the critical points of the Morse function. We survey this relation and discuss some implications, including the finite subset of the spectral package referred to as the "virtually small spectral package" .

arXiv comment18 pages; few misprints in the previous version corrected

References in corpus (2)

• On the topology and analysis of a closed one form. I (Novikov's theory revisited)
• On the Space of Trajectories of a Generic Vector Field