Witten deformation and the spectral package of a Riemannian manifold

Dan Burghelea

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arXiv · 2002.10150

Witten deformation and the spectral package of a Riemannian manifold

Dan Burghelea

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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" .

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Dan Burghelea. 2020-02-24. Witten deformation and the spectral package of a Riemannian manifold. https://arxiv.org/abs/2002.10150

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