Asymptotically rigid mapping class groups and Thompson groups
Louis FunarUniversité Grenoble I, Saint Martin d'Hères, France
Christophe KapoudjianUniversité Paul Sabatier, Toulouse, France
Vlad SergiescuUniversité Grenoble I, Saint Martin d'Hères, France
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We consider Thompson's groups from the perspective of mapping class groups of surfaces of infinite type. This point of view leads us to the braided Thompson groups, which are extensions of Thompson’s groups by infinite (spherical) braid groups. We will outline the main features of these groups and some applications to the quantization of Teichmüller spaces. The chapter provides an introduction to the subject with an emphasis on some of the authors results.