2004/07/31 by Francis Bonahon, Xiaobo Liu · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Braid group #Connection (principal bundle) #Geometric and Algebraic Topology #Geometry #Group (periodic table) #Homomorphism #Ideal (ethics) #Mapping class group #Mathematical analysis #Mathematics #Polynomial #Pure mathematics #Space (punctuation) #Surface (topology) #Teichmüller space #math.GT #math.QA #msc:20G42 #msc:57M50 #msc:57R56
paper · pdf · doi:10.2140/gt.2007.11.889
published as Geom. Topol. 11 (2007) 889-937 · Revised introduction. To appear in Geometry & Topology
arxiv created 2007/03/27 · openalex publication_date 2007/05/27 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract. — We investigate the representation theory of the polynomial core T q S of the quantum Teichmüller space of a punctured surface S. This is a purely algebraic object, closely related to the combinatorics of the simplicial complex of ideal cell decompositions of S. Our main result is that irreducible finite-dimensional representations of T q S are classified, up to finitely many choices, by group homomorphisms from the fundamental group π1(S) to the isometry group of the hyperbolic 3–space H3. We exploit this connection between algebra and hyperbolic geometry to exhibit invariants of diffeomorphisms of S. Contents