LEADER 03048nam 22004095a 450 001 9910151928103321 005 20111229234510.0 010 $a3-03719-575-4 024 70$a10.4171/075 035 $a(CKB)3710000000953877 035 $a(CH-001817-3)144-111229 035 $a(PPN)178156027 035 $a(EXLCZ)993710000000953877 100 $a20111229j20120102 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDecorated Teichmu?ller Theory$b[electronic resource] /$fRobert C. Penner 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2012 215 $a1 online resource (377 pages) 225 0 $aThe QGM Master Class Series (QGM) 330 $aThere is an essentially "tinker-toy" model of a trivial bundle over the classical Teichmu?ller space of a punctured surface, called the decorated Teichmu?ller space, where the fiber over a point is the space of all tuples of horocycles, one about each puncture. This model leads to an extension of the classical mapping class groups called the Ptolemy groupoids and to certain matrix models solving related enumerative problems, each of which has proved useful both in mathematics and in theoretical physics. These spaces enjoy several related parametrizationsleading to a rich and intricate algebro-geometric structure tied to the already elaborate combinatorial structure of the tinker-toy model. Indeed, the natural coordinates give the prototypical examples not only of cluster algebras but also of tropicalization. This interplay of combinatorics and coordinates admits further manifestations, for example, in a Lie theory for homeomorphisms of the circle, in the geometry underlying the Gauss product, in profinite and pronilpotent geometry, in the combinatorics underlying conformal and topological quantum field theories, and in the geometry and combinatorics of macromolecules. This volume gives the story and wider context of these decorated Teichmu?ller spaces as developed by the author over the last two decades in a series of papers, some of them in collaboration. Sometimes correcting errors or typos, sometimes simplifying proofs and sometimes articulating more general formulations than the original research papers, this volume is self-contained and requires little formal background. Based on a master's course at Aarhus University, it gives the first treatment of these works in monographic form. 606 $aComplex analysis$2bicssc 606 $aFunctions of a complex variable$2msc 606 $aSeveral complex variables and analytic spaces$2msc 615 07$aComplex analysis 615 07$aFunctions of a complex variable 615 07$aSeveral complex variables and analytic spaces 686 $a30-xx$a32-xx$2msc 700 $aPenner$b Robert C.$01070707 801 0$bch0018173 906 $aBOOK 912 $a9910151928103321 996 $aDecorated Teichmu?ller Theory$92564803 997 $aUNINA