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The Asymptotics of the $L^2$-analytic Torsion on CR Manifolds with $S^1$ Action
by Rung-Tzung Huang   Guokuan Shao

Vol. 14 No. 4 (2019) P.461~P.491
 DOI: https://doi.org/10.21915/BIMAS.2019403 10.21915/BIMAS.2019403

ABSTRACT

Let $\widetilde{X}$ be a paracompact CR manifold with a transversal CR $S^1$-action, such that there is a discrete group $\Gamma$ acting freely on $\widetilde{X}$ having $X = \widetilde{X}/\Gamma$. We introduce the Fourier components of the $L^2$-Ray-Singer analytic torsion on $\widetilde{X}$ with respect to the $S^1$-action. We establish an asymptotic formula for the Fourier components of the $L^2$-analytic torsion with respect to the $S^1$-action.

KEYWORDS
Determinant, Ray-Singer torsion, CR manifolds

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: Primary: 58J52, 58J28; Secondary: 57Q10

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