L~2-torsion invariants of a surface bundle over S~1

摘要

In the present paper, we introduce L~2-torsion invariants τ_k (k ≥ 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.