02956nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100003200207245007700239260008200316300003400398336002600432337002600458338003600484347002400520490003800544506006600582520173500648650002902383650004102412650005502453856003202508856006602540144-111229CH-001817-320111229234510.0a fot ||| 0|cr nn mmmmamaa111229e20120102sz fot ||| 0|eng d a978303719575870a10.4171/0752doi ach0018173 7aPBKD2bicssc a30-xxa32-xx2msc1 aPenner, Robert C.,eauthor.10aDecorated Teichmüller Theoryh[electronic resource] /cRobert C. Penner3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (377 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aThe QGM Master Class Series (QGM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThere is an essentially “tinker-toy” model of a trivial bundle over the classical Teichmüller space of a punctured surface, called the decorated Teichmüller 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 Teichmüller
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.07aComplex analysis2bicssc07aFunctions of a complex variable2msc07aSeveral complex variables and analytic spaces2msc40uhttps://doi.org/10.4171/075423cover imageuhttps://www.ems-ph.org/img/books/penner_mini.jpg