L2-torsion invariants of a surface bundle over S1

Abstract

In the present paper, we introduce $L^2$-torsion invariants ${\tau }_k(k\ge 1)$ 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 $L^2$-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.