Hyperbolic Groups That Are Not Commensurably Co-Hopfian

Stark, Emily; Woodhouse, Daniel J.

doi:10.1093/imrn/rnaa033

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2021

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Cited by 2 publications

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“…As an aside, this implies that hyperbolic groups which attain their conformal dimension satisfy a kind of "co-Hopfian" property; compare the variations discussed in Kapovich-Lukyanenko [27] and Stark-Woodhouse [38]. (The second author thanks Woodhouse for asking him this question.…”

Section: Bound (I)mentioning

confidence: 99%

Conformal dimension of hyperbolic groups that split over elementary subgroups

Carrasco

Mackay

2021

Invent. math.

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We study the (Ahlfors regular) conformal dimension of the boundary at infinity of Gromov hyperbolic groups which split over elementary subgroups. If such a group is not virtually free, we show that the conformal dimension is equal to the maximal value of the conformal dimension of the vertex groups, or 1, whichever is greater, and we characterise when the conformal dimension is attained. As a consequence, we are able to characterise which Gromov hyperbolic groups (without 2-torsion) have conformal dimension 1, answering a question of Bonk and Kleiner.

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Section: Bound (I)mentioning

confidence: 99%

Conformal dimension of hyperbolic groups that split over elementary subgroups

Carrasco

Mackay

2021

Invent. math.

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“…By Sykiotis [27], the answer is negative if G has a JSJ decomposition with a maximal hanging Fuchsian group. Surprisingly, Stark-Woodhouse [26] found examples of one-ended hyperbolic groups with isomorphic finite-index and infinite-index subgroups.…”

Section: Introductionmentioning

confidence: 99%

Volume vs. Complexity of Hyperbolic Groups

Lazarovich¹

2021

Preprint

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We prove that for a one-ended hyperbolic graph X, the size of the quotient X G by a group G acting freely and cocompactly bounds from below the number of simplices in an Eilenberg-MacLane space for G. We apply this theorem to show that one-ended hyperbolic cubulated groups (or more generally, one-ended hyperbolic groups with globally stable cylinders à la Rips-Sela) cannot contain isomorphic finite-index subgroups of different indices.

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Hyperbolic Groups That Are Not Commensurably Co-Hopfian

Cited by 2 publications

References 23 publications

Conformal dimension of hyperbolic groups that split over elementary subgroups

Conformal dimension of hyperbolic groups that split over elementary subgroups

Volume vs. Complexity of Hyperbolic Groups

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