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Alvarez, Aurélien; Lafforgue, Vincent

doi:10.1016/j.exmath.2016.06.005

Cited by 7 publications

(11 citation statements)

References 14 publications

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“…Specifically, theorem 2 yields a non-elementary hyperbolic quotient Q, which in turn admits a proper affine isometric action on L q (∂Q × ∂Q) and q (Q × Q), by [4,26,31], for sufficiently large q.…”

Section: Residual Properties Of Mapping Class Groups In Low Complexitymentioning

confidence: 99%

Dehn filling Dehn twists

Dahmani¹,

Hagen²,

Sisto³

2020

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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Let $\Sigma _{g,p}$ be the genus–g oriented surface with p punctures, with either g > 0 or p > 3. We show that $MCG(\Sigma _{g,p})/DT$ is acylindrically hyperbolic where DT is the normal subgroup of the mapping class group $MCG(\Sigma _{g,p})$ generated by $K^{th}$ powers of Dehn twists about curves in $\Sigma _{g,p}$ for suitable K. Moreover, we show that in low complexity $MCG(\Sigma _{g,p})/DT$ is in fact hyperbolic. In particular, for 3g − 3 + p ⩽ 2, we show that the mapping class group $MCG(\Sigma _{g,p})$ is fully residually non-elementary hyperbolic and admits an affine isometric action with unbounded orbits on some $L^q$ space. Moreover, if every hyperbolic group is residually finite, then every convex-cocompact subgroup of $MCG(\Sigma _{g,p})$ is separable. The aforementioned results follow from general theorems about composite rotating families, in the sense of [13], that come from a collection of subgroups of vertex stabilizers for the action of a group G on a hyperbolic graph X. We give conditions ensuring that the graph X/N is again hyperbolic and various properties of the action of G on X persist for the action of G/N on X/N.

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Section: Residual Properties Of Mapping Class Groups In Low Complexitymentioning

confidence: 99%

Dehn filling Dehn twists

Dahmani¹,

Hagen²,

Sisto³

2020

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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“…( [AL,3.4]. Consider y in a geodesic [a, u] such that d(a, y) = d(a, v), and an edge e of [u, a] with origin y.…”

Section: Working In Relatively Hyperbolic Groupsmentioning

confidence: 99%

“…We will now see some useful properties, namely that these sets are finite, stable (analogue of [AL,3.3] and [AL,3.4]), non-empty and slices at large angles are reduced to a point. Proposition 1.13.…”

Section: Working In Relatively Hyperbolic Groupsmentioning

confidence: 99%

Proper actions on ℓ p -spaces for relatively hyperbolic groups

Chatterji¹,

Dahmani²

2020

Annales Henri Lebesgue

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“…Example 3 (Alvarez-Lafforgue [AL17]). Let X be the Cayley graph of a Gromov hyperbolic group, with its graph metric and counting measure.…”

Section: Tangent Bundle On a Metric Spacementioning

confidence: 99%

“…This idea has been generalized using a coarse version of "taking the neighbor closest to 1". The constructions involved in [Yu05] and in [AL17] use a coarse geodesic flow from 1 to h and from g to h and the comparison of the arrivals of these flows. In free groups, they arrive exactly at the same point if h is not on the segment [1, g], but in hyperbolic groups, there could be a difference.…”

Section: Introductionmentioning

confidence: 99%

Tangent bundles of hyperbolic spaces and proper affine actions on $L^p$ spaces

Chatterji,

Dahmani,

Haettel

et al. 2019

Preprint

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Actions affines isométriques propres des groupes hyperboliques sur des espaces ℓp

Cited by 7 publications

References 14 publications

Dehn filling Dehn twists

Dehn filling Dehn twists

Proper actions on ℓ p -spaces for relatively hyperbolic groups

Tangent bundles of hyperbolic spaces and proper affine actions on $L^p$ spaces

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