Title: 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.