  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.

Group Theory