$L^2$-Euler characteristics and the Thurston norm

Abstract

We assign to a finite $CW$-complex and an element in its first cohomology group a twisted version of the $L^2$-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 will use the $L^2$-Euler characteristic to address the problem whether the existence of a map inducing an epimorphism on fundamental groups implies an inequality of the Thurston norms.

44 pages, updated references, incorporated comments by the referee

References in corpus (1)

• Alexander and Thurston norms, and the Bieri-Neumann-Strebel invariants for free-by-cyclic groups

Cited by in corpus (2)

• Survey on L^2-invariants and 3-manifolds
• The agrarian polytope of two-generator one-relator groups