## Journal of the Mathematical Society of Japan

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

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 18 January 2017

https://projecteuclid.org/euclid.jmsj/1484730028

Digital Object Identifier
doi:10.2969/jmsj/06910311

Mathematical Reviews number (MathSciNet)
MR3597557

Zentralblatt MATH identifier
1369.58025

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

#### Citation

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. https://projecteuclid.org/euclid.jmsj/1484730028

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