Dehn filling Dehn twists

François Dahmani, Mark Hagen, Alessandro Sisto

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
17 Downloads (Pure)


Let be the genus-g oriented surface with p punctures, with either g > 0 or p > 3. We show that is acylindrically hyperbolic where DT is the normal subgroup of the mapping class group generated by powers of Dehn twists about curves in for suitable K.Moreover, we show that in low complexity is in fact hyperbolic. In particular, for 3g - 3 + p 1/2 2, we show that the mapping class group is fully residually non-elementary hyperbolic and admits an affine isometric action with unbounded orbits on some space. Moreover, if every hyperbolic group is residually finite, then every convex-cocompact subgroup of 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.

Original languageEnglish
Pages (from-to)28-51
Number of pages24
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Issue number1
Early online date30 Jan 2020
Publication statusPublished - Feb 2021


  • Dehn twists
  • Mapping class groups

ASJC Scopus subject areas

  • General Mathematics


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