An Extension of a Theorem by Cheeger and Müller to Spaces with Isolated Conical Singularities

Abstract: An important comparison theorem in global analysis is the comparison of analytic and topological torsion for smooth compact manifolds equipped with a unitary flat vector bundle. It has been conjectured by Ray and Singer and has been independently proved by Cheeger and Mu ̈ller in the 70ies. Bismut and Zhang combined the Witten deformation and local index techniques to generalise the result of Cheeger and Mu ̈ller to arbitrary flat vector bundles with arbitrary Hermitian metrics. The aim of this talk is to present an extension of the Cheeger-Mu ̈ller theorem to spaces with isolated conical singularities by generalising the proof of Bismut and Zhang to the singular setting.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

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