R torsion and analytic torsion for a conical frustum

TL;DR

This paper studies the behavior of R torsion on a conical frustum as one boundary shrinks, revealing that the limit corresponds to the intersection torsion of the cone formed.

Contribution

It establishes a connection between the R torsion of a conical frustum and the intersection torsion of the resulting cone through a regularization process.

Findings

Limit of R torsion equals intersection torsion for the cone

Regularization is necessary for the limit process

Provides a new link between torsion invariants

Abstract

We investigate the limit the R torsion of a conical frustum as one of the basis is shrunk to a point. We show that, if we take suitable regularization, such a limit gives the intersection torsion of the resulting cone.