BooksirmaCollected Volumepp. 595–664

Asymptotically rigid mapping class groups and Thompson groups

  • Louis Funar

    Université Grenoble I, Saint Martin d'Hères, France

  • Christophe Kapoudjian

    Université Paul Sabatier, Toulouse, France

  • Vlad Sergiescu

    Université Grenoble I, Saint Martin d'Hères, France
Asymptotically rigid mapping class groups and Thompson groups cover

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Abstract

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.