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

Ursula Ludwig (Universität Duisburg-Essen)
Wednesday, 9 December, 2020 | 15:00–16:00 | Zoom
Contact: Benjamin Alvarez, Polyxeni Spilioti

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 Müller in the 70ies. Bismut and Zhang combined the Witten deformation and local index techniques to generalise the result of Cheeger and Müller to arbitrary flat vector bundles with arbitrary Hermitian metrics.The aim of this talk is to present an extension of the Cheeger-Müller theorem to spaces with isolated conical singularities by generalising the proof of Bismut and Zhang to the singular setting. In the first part of the talk I will recall the classical Cheeger-Müller theorem on a compact smooth manifold.

The talk will be given on Zoom. Please, contact the organizers for more information.

Organised by: Seminar of the Young Mathematicians of Aarhus