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Linearity and indiscreteness of amalgamated products of hyperbolic groups

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arxiv 2112.05574 v2 pith:3XT4LDLZ submitted 2021-12-10 math.GR

Nicolas Tholozan , Konstantinos Tsouvalas This is my paper · ORCID
classification math.GR
keywords groupsamalgamatedexampleslinearlinearityproductsword-hyperbolicadmit
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We discuss the linearity and discreteness of amalgamated products of linear word-hyperbolic groups. In particular, we prove that the double of an Anosov group along a maximal cyclic subgroup is always linear, and we construct examples of such groups which do not admit any discrete and faithful representation in rank 1. We also build new examples of non-linear word-hyperbolic groups, elaborating on a previous work of Canary--Stover--Tsouvalas.

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  1. Bordered hyperbolic manifolds with a fixed perimeter-to-volume ratio

    math.GT 2026-07 accept novelty 6.5 of 10

    For every n≥3 there are infinitely many pairwise incommensurable finite-volume hyperbolic n-manifolds with totally geodesic boundary sharing one fixed perimeter-to-volume ratio.

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