04492nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400220018424500940020626000820030030000340038233600260041633700260044233800360046834700240050449000830052850515670061150600660217852016260224465000290387065000410389965000550394070000370399585600320403285600660406455-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20070525sz fot ||| 0|eng d a978303719529170a10.4171/0292doi ach0018173 7aPBKD2bicssc a30-xxa32-xx2msc10aHandbook of Teichmüller Theory, Volume Ih[electronic resource] /cAthanase Papadopoulos3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2007 a1 online resource (802 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v1100tIntroduction to Teichmüller theory, old and new /rAthanase Papadopoulos --tHarmonic maps and Teichmüller theory /rGeorgios D. Daskalopoulos, Richard A. Wentworth --tOn Teichmüller’s metric and Thurston’s asymmetric metric on Teichmüller space /rAthanase Papadopoulos, Guillaume Théret --tSurfaces, circles, and solenoids /rRobert C. Penner --tAbout the embedding of Teichmüller space in the space of geodesic Hölder distributions /rJean-Pierre Otal --tTeichmüller spaces, triangle groups and Grothendieck dessins /rWilliam J. Harvey --tOn the boundary of Teichmüller disks in Teichmüller and in Schottky space /rFrank Herrlich, Gabriela Schmithüsen --tIntroduction to mapping class groups of surfaces and related groups /rShigeyuki Morita --tGeometric survey of subgroups of mapping class groups /rJohn Loftin --tDeformations of Kleinian groups /rAlbert Marden --tGeometry of the complex of curves and of Teichmüller space /rUrsula Hamenstädt --tParameters for generalized Teichmüller spaces /rCharalampos Charitos, Ioannis Papadoperakis --tOn the moduli space of singular euclidean surfaces /rMarc Troyanov --tDiscrete Riemann surfaces /rChristian Mercat --tOn quantizing Teichmüller and Thurston theories /rLeonid Chekhov, Robert C. Penner --tDual Teichmüller and lamination spaces /rVladimir V. Fock, Alexander Goncharov --tAn analog of a modular functor from quantized Teichmüller theory /rJörg Teschner --tOn quantum moduli space of flat PSL2(ℝ)-connections on a punctured surface /rRinat Kashaev.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe Teichmüller space of a surface was introduced by O. Teichmüller
in the 1930s. It is a basic tool in the study of Riemann's moduli
space and of the mapping class group. These objects are fundamental
in several fields of mathematics including algebraic geometry,
number theory, topology, geometry, and dynamics.
The original setting of Teichmüller theory is complex analysis.
The work of Thurston in the 1970s brought techniques of hyperbolic
geometry in the study of Teichmüller space and of its asymptotic
geometry. Teichmüller spaces are also studied from the point of view
of the representation theory of the fundamental group of the surface
in a Lie group G, most notably G = PSL(2,ℝ) and G = PSL(2,ℂ).
In the 1980s, there evolved an essentially combinatorial treatment of
the Teichmüller and moduli spaces involving techniques and ideas
from high-energy physics, namely from string theory. The current
research interests include the quantization of Teichmüller space, the
Weil–Petersson symplectic and Poisson geometry of this space as well
as gauge-theoretic extensions of these structures. The quantization
theories can lead to new invariants of hyperbolic 3-manifolds.
The purpose of this handbook is to give a panorama of some of
the most important aspects of Teichmüller theory. The handbook
should be useful to specialists in the field, to graduate students,
and more generally to mathematicians who want to learn about the
subject. All the chapters are self-contained and have a pedagogical
character. They are written by leading experts in the subject.07aComplex analysis2bicssc07aFunctions of a complex variable2msc07aSeveral complex variables and analytic spaces2msc1 aPapadopoulos, Athanase,eeditor.40uhttps://doi.org/10.4171/029423cover imageuhttps://www.ems-ph.org/img/books/irma11_mini.jpg