2003/02/25 by Christophe Kapoudjian, C. Kapoudjian, Kapoudjian, C. +3
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT
paper · pdf · doi:10.48550/arxiv.math/0302300
arxiv created 2003/02/25 · openalex publication_date 2003/02/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study some aspects of the geometric representation theory of the Thompson and Neretin groups, suggested by their analogies with the diffeomorphism groups of the circle. We prove that the Burau representation of the Artin braid groups extends to a mapping class group AT related to Thompson's group T by a short exact sequence B∞\hookrightarrow AT→ T, where B∞ is the infinite braid group. This \it non-commutative extension abelianises to a central extension 0→ \Z→ AT/[B∞,B∞]→ T→ 1 detecting the \it discrete version gv of the Bott-Virasoro-Godbillon-Vey class. A morphism from the above non-commutative extension to a reduced Pressley-Segal extension is then constructed, and the class gv is realised as a pull-back of the reduced Pressley-Segal class. A similar program is carried out for an extension of the Neretin group related to the \it combinatorial version of the Bott-Virasoro-Godbillon-Vey class.