Journal of the Mathematical Society of Japan

The analytic torsion of the finite metric cone over a compact manifold


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We give an explicit formula for the $L^2$ analytic torsion of the finite metric cone over an oriented compact connected Riemannian manifold. We provide an interpretation of the different factors appearing in this formula. We prove that the analytic torsion of the cone is the finite part of the limit obtained collapsing one of the boundaries, of the ratio of the analytic torsion of the frustum to a regularising factor. We show that the regularising factor comes from the set of the non square integrable eigenfunctions of the Laplace Beltrami operator on the cone.

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J. Math. Soc. Japan, Volume 69, Number 1 (2017), 311-371.

First available in Project Euclid: 18 January 2017

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Primary: 58J52: Determinants and determinant bundles, analytic torsion

analytic torsion pseudo manifolds finite metric cone


HARTMANN, Luiz; SPREAFICO, Mauro. The analytic torsion of the finite metric cone over a compact manifold. J. Math. Soc. Japan 69 (2017), no. 1, 311--371. doi:10.2969/jmsj/06910311.

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