Abstract
Let be the genusg 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 nonelementary hyperbolic and admits an affine isometric action with unbounded orbits on some space. Moreover, if every hyperbolic group is residually finite, then every convexcocompact 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 language  English 

Journal  Proceedings of the Royal Society of Edinburgh Section A: Mathematics 
Early online date  30 Jan 2020 
DOIs  
Publication status  Epub ahead of print  30 Jan 2020 
Keywords
 Dehn twists
 Mapping class groups
ASJC Scopus subject areas
 Mathematics(all)
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Alessandro Sisto
 School of Mathematical & Computer Sciences  Assistant Professor
 School of Mathematical & Computer Sciences, Mathematics  Assistant Professor
Person: Academic (Research & Teaching)