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Talk

November 3rd 2020
Jean Raimbault (Université Toulouse III, France): L^2-torsion on the character variety

Abstract

The $L^2$-torsion of a CW complex with coefficients in an arbitrary local system is not well-defined in general. In this talk I will explain why it is OK for $\mathrm{SL}_2(\CC)$-representations of the fundamental group of a finite-volume hyperbolic manifold which lie close enough to the holonomy representation of the hyperbolic structure, study the regularity properties of this $L^2$-torsion as a function on the variety of $\mathrm{SL}_2(\CC)$-representations and make some remarks as to its relation with geometric invariants.

This is joint work with Léo Bénard.

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