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

Dahmani, François¹

¹ Institut Fourier, Université Grenoble Alpes, Grenoble, France

Geometry & topology, Tome 22 (2018) no. 7, pp. 4113-4144.

Résumé

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 consist 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.

Détail

DOI : 10.2140/gt.2018.22.4113

Classification : 20E07, 20F65
Keywords: Dehn twist, mapping class group, rotating families, projection complexes

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