A special value of Ruelle L-function and the theorem of Cheeger and Muller

The Equivariant Cheeger-Müller Theorem on Locally Symmetric Spaces

In this paper, we provide a concrete interpretation of equivariant Reidemeister torsion and demonstrate that Bismut-Zhang's equivariant Cheeger-Müller theorem simplifies considerably when applied to locally symmetric spaces. In a companion paper, this allows us to extend recent results on torsion cohomology growth and torsion cohomology comparison for arithmetic locally symmetric spaces an equivariant setting.

An $L^2$-Cheeger Müller theorem on compact manifolds-with-boundary

We generalize a Cheeger-Müller type theorem for flat, unitary bundles on infinite covering spaces over manifolds-with-boundary, proven by Burghelea, Friedlander and Kappeller arXiv:dg-ga/9510010 [math.DG]. Employing recent anomaly results by Brüning, Ma and Zhang, we prove an analogous statement for a general flat bundle that is only required to have a unimodular restriction to the boundary.

An extension of the Cheeger-Müller theorem for a cone

We prove the equality of the $L^2$-analytic torsion and the intersection R torsion of the even dimensional finite metric cone over an odd dimensional compact manifold.

On the anomaly terms in Cheeger-Müller theorem on spaces with conical singularities

We prove that the anomaly term appearing in the ratio between Reidemeister torsion and analytic torsion for a space with a conical singularity vanishes in the smooth case. Moreover, we show that such anomaly term is non trivial for the cone over a torus.

A Cheeger-Müller theorem for manifolds with wedge singularities

We study the spectrum and heat kernel of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold degenerating to a manifold with wedge singularities. Provided the Hodge Laplacians in the fibers of the wedge have an appropriate spectral gap, we give uniform constructions of the resolvent and heat kernel on suitable manifolds with corners. When the wedge manifold and the base of the wedge are odd dimensional, this is used to obtain a Cheeger-Müller theorem relating analytic torsion with the Reidemeister torsion of the natural compactification by a manifold with boundary.

沿嵌入子流形的楔形奇点的Cheeger-Müller定理

Cheeger-Müller theorem for a wedge singularity along an embedded submanifold

本文证明了在沿偶余维嵌入子流形构造的楔形奇点空间上，解析Reidemeister挠率与相交Reidemeister挠率相等，推广了Cheeger-Müller定理。