Wolfgang Lück: Universal L2-torsion, L2-Euler characteristics, Thurston norms and polytopes

We assign to a finite CW-complex and a cocycle in its first cohomology a twisted version of the L2-Euler characteristic and study its main properties. In the case of an irreducible orientable 3-manifold with empty or toroidal boundary and infinite fundamental group we identify it with the Thurston norm. We discuss its relation to the degree of higher order Alexander polynomials in the sense of Cochran and Harvey.

All these invariants come from another invariant called universal L2-torsion, which can be related to the Grothendieck groups of integral polytopes in ℝn under the Minkowski sum.

This is a joint project with Stefan Friedl.

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology and the Workshop: New directions in L2-invariants (07.09.2016)