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The asymptotics of the \(L^2\)-analytic torsion on CR manifolds with \(S^1\) action. (English) Zbl 1448.58029

Authors’ abstract: Let \(X\) be a compact connected CR manifold of dimension \(2n+1\), \(n\geq 1\). 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.

MSC:

58J52 Determinants and determinant bundles, analytic torsion
58J28 Eta-invariants, Chern-Simons invariants
57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
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