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001			144-111229
003			CH-001817-3
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008			111229e20120102sz fot ||| 0|eng d
020			_a9783037195758
024	7	0	_a10.4171/075 _2doi
040			_ach0018173
072		7	_aPBKD _2bicssc
084			_a30-xx _a32-xx _2msc
100	1		_aPenner, Robert C., _eauthor.
245	1	0	_aDecorated Teichmüller Theory _h[electronic resource] / _cRobert C. Penner
260	3		_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2012
264		1	_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2012
300			_a1 online resource (377 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	0		_aThe QGM Master Class Series (QGM)
506	1		_aRestricted to subscribers: _uhttp://www.ems-ph.org/ebooks.php
520			_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 parametrizations leading 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.
650	0	7	_aComplex analysis _2bicssc
650	0	7	_aFunctions of a complex variable _2msc
650	0	7	_aSeveral complex variables and analytic spaces _2msc
700	1		_aPenner, Robert C., _eauthor.
856	4	0	_uhttps://doi.org/10.4171/075
856	4	2	_3cover image _uhttp://www.ems-ph.org/img/books/penner_mini.jpg
942			_2EBK13818 _cEBK
999			_c50442 _d50442