The leading coefficient of the L 2 -Alexander torsion

Abstract

We give upper and lower bounds on the leading coefficients of the L-2-Alexander torsions of a 3-manifold M in terms of hyperbolic volumes and of relative L-2-torsions of sutured manifolds obtained by cutting M along certain surfaces. We prove that for numerous families of knot exteriors the lower and upper bounds are equal, notably for exteriors of 2-bridge knots. In particular we compute the leading coefficient explicitly for 2-bridge knots.