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arXiv · 2203.11996

Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity

Sam Hughes·Motiejus Valiunas
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Abstract

We construct a CAT(0) hierarchically hyperbolic group (HHG) acting geometrically on the product of a hyperbolic plane and a locally-finite tree which is not biautomatic. This gives the first example of an HHG which is not biautomatic, the first example of a non-biautomatic CAT(0) group of flat-rank 2, and the first example of an HHG which is injective but not Helly. Our proofs heavily utilise the space of geodesic currents for a hyperbolic surface.

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Sam Hughes, Motiejus Valiunas. 2022-03-22. Commensurating HNN-extensions: hierarchical hyperbolicity and biautomaticity. https://doi.org/10.4171/cmh/572

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