Twisting $L^2$-invariants with finite-dimensional representations

Abstract

We investigate how one can twist L^2-invariants such as L^2-Betti numbers and L^2-torsion with finite-dimensional representations. As a special case we assign to the universal covering of a finite connected CW-complex X together with an element phi in H^1(X;R) a phi-twisted L^2-torsion function from R^{>0} to R, provided that the fundamental group of X is residually finite and its universal covering is L^2-acyclic.

77 pages, final version, to appear in Journal of Topology and Analysis

References in corpus (6)

• The K-theoretic Farrell-Jones Conjecture for hyperbolic groups
• Completion of the Proof of the Geometrization Conjecture
• $L^2$-Alexander invariant for knots
• Degree of $L^2$-Alexander torsion for 3-manifolds
• Splitting the relative assembly map, Nil-terms and involutions
• Survey on approximating L^2-invariants by their classical counterparts: Betti numbers, torsion invariants and homological growth

Cited by in corpus (10)

• Degree of $L^2$-Alexander torsion for 3-manifolds
• Survey on approximating L^2-invariants by their classical counterparts: Betti numbers, torsion invariants and homological growth
• $L^2$-Euler characteristics and the Thurston norm
• Survey on L^2-invariants and 3-manifolds
• Gluing formulas for the $L^2$-Alexander torsions
• Lehmer's Problem for arbitrary groups
• ${\ell }^2$-torsion of free-by-cyclic groups
• On the positivity of twisted $L^2$-torsion for 3-manifolds
• Limits of Mahler measures in multiple variables
• $L^2$-Burau maps and $L^2$-Alexander torsions