The analytic torsion of a cone over a sphere

TL;DR

This paper calculates the analytic torsion for cones over spheres of dimensions 1 to 3 and proposes a general formula for cones over odd-dimensional spheres, advancing understanding in geometric analysis.

Contribution

It provides explicit computations of analytic torsion for low-dimensional cones over spheres and conjectures a universal formula for higher odd dimensions.

Findings

Computed analytic torsion for cones over spheres of dimensions 1, 2, and 3.

Proposed a conjecture for the general formula of analytic torsion over odd-dimensional spheres.

Enhanced understanding of spectral invariants in geometric analysis.

Abstract

We compute the analytic torsion of a cone over a sphere of dimension 1, 2, and 3, and we conjecture a general formula for the cone over an odd dimensional sphere.