The leading coefficient of the L²-Alexander torsion

2018/06/28 by Aribi, Fathi Ben, Friedl, Stefan, Herrmann, Gerrit · 1 citation
#57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1806.10965

Abstract

We give upper and lower bounds on the leading coefficients of the L²-Alexander torsions of a 3-manifold M in terms of hyperbolic volumes and of relative L²-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.

Cited by

• Universal L²-torsion and sutured decomposition for 3-manifolds

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