The leading coefficient of the $L^2$-Alexander torsion

Fathi Ben Aribi; Stefan Friedl; Gerrit Herrmann

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arXiv · 1806.10965

The leading coefficient of the $L^2$-Alexander torsion

Fathi Ben Aribi·Stefan Friedl·Gerrit Herrmann

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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.

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Fathi Ben Aribi, Stefan Friedl, Gerrit Herrmann. 2018-06-28. The leading coefficient of the $L^2$-Alexander torsion. https://arxiv.org/abs/1806.10965

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