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arXiv · 2510.20959

$L^2$-torsion of automorphisms

Sam Hughes·Wolfgang Lueck
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Abstract

We develop the theory of $L^2$-torsion of an automorphism of a group and compute it for every automorphism of a group which is hyperbolic and one-ended relative to a finite collection of virtually polycyclic groups. We also prove a combination formula for the $L^2$-torsion of a group in terms of the $L^2$-torsion of its stabilisers of a sufficiently nice action on a contractible space. We apply it to compute the $L^2$-torsion of a selection of CAT(0) lattices, of many relatively hyperbolic groups and their automorphisms, of higher dimensional graph manifolds, and of handlebody groups.

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Sam Hughes, Wolfgang Lueck. 2025-10-23. $L^2$-torsion of automorphisms. https://arxiv.org/abs/2510.20959

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