2011/11/30 by Leonid Chekhov, Michael Shapiro · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Class (philosophy) #Cluster algebra #Geodesic #Geometric and Algebraic Topology #Graph #Orbifold #Order (exchange) #Reciprocal #Riemann surface #Type (biology) #math-ph #math.CO #math.MP #msc:13F60 #msc:53D30
paper · pdf · doi:10.1093/imrn/rnt016
published as Int Math Res Notices (2014) Vol. 2014 2746-2772 · 20 pages, notations and many essential typos corrected, most significantly, formulae 2.3, 2.5, proof of Lemmata 2.6 and 4.5. Journal reference is added (published version contains typos)
openalex publication_date 2013/02/08 · arxiv created 2014/08/21 · arxiv updated 2014/08/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We define a new generalized class of cluster-type mutations for which exchange transformations are given by reciprocal polynomials. In the case of second-order polynomials of the form these transformations are related to triangulations of Riemann surfaces of arbitrary genus with at least one hole/puncture and with an arbitrary number of orbifold points of arbitrary integer orders no. In the second part of the paper, we propose the dual graph description of the corresponding Teichmüller spaces, construct the Poisson algebra of the Teichmüller space coordinates, propose the combinatorial description of the corresponding geodesic functions and find the mapping class group transformations thus providing the complete description of the above Teichmüller spaces.