Let be an oriented irreducible 3-manifold with infinite fundamental group and empty or toroidal boundary which is not . Consider any element in the first cohomology of with integer coefficients. Then one can define the -twisted -torsion function of the universal covering which is a function from the set of positive real numbers to the set of real numbers. By earlier work of the second author and Schick the evaluation at determines the volume.
In this paper we show that the degree of the -torsion function, which is a number extracted from its asymptotic behavior at 0 and at , agrees with the Thurston norm of .
Cite this article
Stefan Friedl, Wolfgang Lück, The -torsion function and the Thurston norm of 3-manifolds. Comment. Math. Helv. 94 (2019), no. 1, pp. 21–52DOI 10.4171/CMH/453