L²-torsion invariants of a surface bundle over S¹

Abstract

In the present paper, we introduce L²-torsion invariants τ_k(k≥q 1) for surface bundles over the circle and investigate them from the view point of the mapping class group of a surface. It is conjectured that they converge to the L²-torsion for the regular representation of the fundamental group. Further we give an explicit and computable formula of the first two invariants by using the Mahler measure.