The L²-torsion for representations of hyperbolic lattices

2020/12/01 by Waßermann, Benjamin
#57Q10 (Secondary) #58J52 (Primary) 53C35 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2012.00380

Abstract

We prove equality of analytic and topological L²-torsion associated with an odd-dimensional finite volume hyperbolic manifold and a representation of the fundamental group which extends to the ambient Lie group. This generalizes a previous result due to Lück and Schick. Alternatively, this result can be regarded as the L²-analogue of recent work by Müller and Rochon.

Related

• Analytic torsion of complete hyperbolic manifolds of finite volume
• L²-torsion of automorphisms
• L²-torsion invariants and the Magnus representation of the mapping class group
• Analytic torsion and L²-torsion of compact locally symmetric manifolds
• Twisted L²-torsion on the character variety