The normal closure of big Dehn twists, and plate spinning with rotating families

Abstract

We study the normal closure of a big power of one or several Dehn twists in a Mapping Class Group. We prove that it has a presentation whose relators consists only of commutators between twists of disjoint support, thus answering a question of Ivanov. Our method is to use the theory of projection complexes of Bestvina Bromberg and Fujiwara, together with the theory of rotating families, simultaneously on several spaces.

32 pages

References in corpus (2)

• Partial periodic quotient of groups acting on a hyperbolic space
• Normal subgroups of mapping class groups and the metaconjecture of Ivanov

Cited by in corpus (6)

• A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups
• Dehn filling Dehn twists
• Right-angled Artin groups as normal subgroups of mapping class groups
• Short hierarchically hyperbolic groups II: quotients and the Hopf property for Artin groups
• Rigidity of mapping class groups mod powers of twists
• Vanishing of the Euler class in Power subgroups of the punctured mapping class group