Universal torsion, L^2-invariants, polytopes and the Thurston norm
Thu, Jul 2, 2015
PIMS, University of British Columbia
PIMS Symposium on the Geometry and Topology of Manifolds
We introduce universal torsion which is defined for -acyclic manifolds with torsion free fundamental group and takes values in certain -groups of a skew field associated to the integral group ring. It encompasses well-know invariants such as the Alexander polynomial and -torsion. We discuss also twisted -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.