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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2510.20959 |
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| _version_ | 1866911544842911744 |
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| author | Hughes, Sam Lueck, Wolfgang |
| author_facet | Hughes, Sam Lueck, Wolfgang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20959 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $L^2$-torsion of automorphisms Hughes, Sam Lueck, Wolfgang Group Theory Primary 20F99, Secondary 46L99 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. |
| title | $L^2$-torsion of automorphisms |
| topic | Group Theory Primary 20F99, Secondary 46L99 |
| url | https://arxiv.org/abs/2510.20959 |