Universal torsion, L^2-invariants, polytopes and the Thurston norm

Author: 
Wolfgang Lück
Date: 
Thu, Jul 2, 2015
Location: 
PIMS, University of British Columbia
Conference: 
PIMS Symposium on the Geometry and Topology of Manifolds
Abstract: 

We introduce universal torsion which is defined for $ L^2 $-acyclic manifolds with torsion free fundamental group and takes values in certain $ K_1 $-groups of a skew field associated to the integral group ring. It encompasses well-know invariants such as the Alexander polynomial and $ L^2 $-torsion. We discuss also twisted $ L^2 $-torsion and higher order Alexander polynomials which can also be derived from the universal invariant and assign certain polytopes to the universal torsion. This gives especially in dimension 3 interesting invariants which recover for instance the Thurston norm.

Notes: