Jun 06, 2006 buy teichmuller theory and applications to geometry, topology, and dynamics on free shipping on qualified orders. Free geometry books download ebooks online textbooks. The third, by hubbard, illustrates the role of these mappings in thurstons. Hyperbolicity in teichmuller space, a knot characterization and 1connected nonnegatively curved 4manifolds with circle symmetry. The theory of higgs bundles, initiated by hitchin, has been instrumental in understanding the topology and geometry of character varieties. Teichmuller theory and applications to geometry, topology. Before developing interuniversal teichmuller theory, mochizuki became wellknown for proving that hyperbolic curves which include, for example, elliptic curves with one point removed, and the projective line with three points removed are anabelian varieties. This section contains free ebooks and guides on geometry, some of the resources in this section can be viewed online and some of them can be downloaded. In the case of a surface with one puncture, the fundamental group is a free. The mantra is studying objects in families gives important information about the individual objects. A panoramic overview of interuniversal teichmuller theory. Get your kindle here, or download a free kindle reading app. Harmonic teichmuller mappings chen, xingdi and fang, ainong, proceedings of the japan academy, series a, mathematical sciences, 2006.
The classification of homeomorphisms of surfaces 2. Talk by luo feng december 27, 2010 let us denote by g. Teichmuller theory and applications to geometry, topology, and. Complex structures, jacobians and the weil petersson form 31 lecture 4. Irma lectures in mathematics and theoretical physics 17 edited by christian kassel and vladimir g. Depending on the approach you take to teichmuller theory, some knowledge of manifolds and differential geometry would also be helpful. Stroock, an introduction to the analysis of paths on a riemannian manifold, 2000 73 john locker, spectral theory of nonselfadjoint twopoint differential operators, 2000. Enter your mobile number or email address below and well send you a link to download the free kindle app. Teichmuller spaces of riemann surfaces, moduli spaces and modular groups. In some cases they can be used to obtain new properties. Teichmuller theory is one of those few wonderful subjects which bring together.
We present a systematic way to generate critically. By using quantum teichm\uller theory, we construct a one parameter family of tqfts on the categroid of admissible leveled shaped 3manifolds. This is a decomposition of into pairs of pants, and to each curve in the decomposition is associated its length in the hyperbolic metric corresponding to the point in teichmuller space, and another real parameter called the. This volume is the second of four volumes devoted to teichmuller theory and its applications to geometry, topology, and dynamics. Prerequisites are the rst year courses in real and complex analysis, or the. Teichmuller theory is one of those few wonderful subjects which bring together, at an equally important. The primary focus of teichmuller theory is riemann surfaces of finite topological type, thus surfaces with g handles, m punctures, and n holes, for some triple of nonnegative integers g,m,n. Interuniversal teichmuller theory i construction of hodge theaters shinichi mochizuki april2020 abstract. Classical teichmuller theory is a topic in complex analysis. We consider classical teichmuller theory and the geodesic flow on the cotangent bundle of the teichmuller space. Poincares theorem and teichmuller theory for open surfaces 357 return now to m2 of the above topological type. We show that the corresponding orbits provide a canonical description of certain 2. Quasiconformal mappings and teichmullers theorem by bers, lipman. So you would need complex analysis and probably real analysis before that.
These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. Stability for infinitedimensional fibre bundles sakai, katsuro, tsukuba journal of mathematics, 1981. It is based on a course i taught at university of utah in 19921993. This course was a prequel to the 19931994 course on thurstons hyperbolization. Teichmuller space encodes the possible number of ways in which you can deform complex structure on a space. Pdf quasiconformal maps and teichmuller theoryextremal. Parametrised databases of surfaces based on teichmuller theory. It is a basic tool in the study of riemanns moduli spaces and the mapping class groups.
Athanase papadopoulos teichmuller theory is one of those few wonderful subjects which bring together, at an equally important level, fundamental ideas coming from different. Printed in great britain the asymptotic geometry of teichmuller space steven p. Then you can start reading kindle books on your smartphone, tablet, or computer no kindle device required. Teichmuller theory and the teichmuller metric, the \classical applications of teichmuller theory to rational maps and kleinian groups, and my own work, in part with mikhail lyubich, on the asymptotic theory of moduli and its applications to conformal dynamical systems. We intentionally remove most bibliographic references from the body of the text devoting a special section to the. Geometry of teichmuller space with the teichmuller metric. On the other hand, the theory may be regarded as a fairly precise hyperbolic analog of the serretate theory of ordinary abelian varieties and their moduli. Kerckhoff received 8 december 1978 introduction teichmuller space is the space of conformal structures on a topological surface mg of genus g where two are equivalent if there is a conformal map between them. This edition contains a large number of additions and corrections scattered throughout the text, including the incorporation of a new chapter on statesp. Volume 5 by athanase papadopoulos, 9783037191606, available at book depository with free delivery worldwide. Tight contact structures on fibred honda, ko, kazez, william h. A road to interuniversal teichmuller theory mathoverflow.
Thats really all you need to pick up an introduction to the subject. Geometry of teichmuller space with the teichmuller metric howard masur january 20, 2010 1 introduction the purpose of this chapter is to describe recent progress in the study of teichmuller geometry. Denote by compgi c compg the subspace of all metrics g compg such that k 1. A theme of much of teichmuller theory is to compare the complex analytic theory where points are given by riemann surfaces and the hyperbolic geometry. Harmonic measure and polynomial julia sets binder, i. The theory of uniformization of \p\adic hyperbolic curves and their moduli was initiated in a previous work by mochizuki. Volumes 2 through 4 prove four theorems by william thurston. Jan 10, 2015 the mantra is studying objects in families gives important information about the individual objects. Teichmuller theory and applications ams bulletin of the american. Teichmuller theory and applications to geometry, topology, and dynamics. Selfcoincidence of fibre maps dold, albrecht and goncalves, daciberg lima, osaka journal of mathematics, 2005. A brief tour of grothendieckteichmuller theory daniel miller september 2, 2014 everything in this brief note is inspired by grothendiecks revolutionary letter gro97. What is a good introduction to teichmuller theory, mapping class groups etc. The original setting of teichmuller theory is complex analysis.
Teichmuller theory and applications volume 1 pdf free download. Our approach is based on ideas that come from teichmuller and moduli space of closed riemann surfaces theory, and the problem of finding a canonical and explicit cell. The asymptotic geometry of teichmuller space sciencedirect. I have tried to make 3 and 4 a little independent from 1 and 2 if one has a little. Theory and methods second edition with 124 illustrations springer. I suspect that this could also be related to this article, though i am not so sure yet how to do that. These notes were written for some expository talks on teichmuller.
The second of four volumes devoted to teichmuller theory and its applications to geometry, topology, and dynamics, this volume proves two theorems by william thurston. Since the correspondence is given by the uniformization theorem, there are rarely exact formulae and one often has to. Teichmuller theory mathematisches institut uni bonn. Some results on the weilpetersson metric of teichm. What are the mathematical prerequisites to understanding.
Introduction an orientation preserving homeomorphism ffrom a riemann surface x onto a riemann surface y is given. A survey of the very important weilpetersson metric can be found in w. Teichmuller theory and applications to geometry, topology, and dynamics volume 1. Teichmuller theory and applications matrix editions. Each point in may be regarded as an isomorphism class of marked riemann surfaces, where a marking is an isotopy class of homeomorphisms from to itself. Teichmuller theory and applications to geometry, topology, and dynamics hardcover june 6, 2006. Gardiner and jun hu proceedings of the year on teichmuller theory hri, allahabad, volume 10, 2009, pages 195228 abstract we present a brief exposition of teichmullers theorem. The fenchelnielsen coordinates so named after werner fenchel and jakob nielsen on the teichmuller space are associated to a pants decomposition of the surface. Towards a modular functor from quantum higher teichmuller theory. See, for example, kiran kedlayas lecture at the 2015 conference on interuniversal teichmuller theory at oxford. These notes were written for some expository talks on teichmuller theory, given.
Ill indicate its broad lines in the next few paragraphs. In this paper we develop a systematic deformation theory for conic constant curvature metrics on a closed surface when all cone. Download fulltext pdf quasiconformal maps and teichmuller theoryextremal mappings, overview article pdf available in bulletin classe des sciences mathematiques et natturalles 14538. By m obius theorem, gand ntogether can classify all the. Harmonic maps from representations to higgs bundles andrew sanders abstract. Therefore the mapping class group acts on free homotopy classes of simple closed. Introduction to teichmuller theory, old and new ems publishing. Superposition, delayed choice, quantum erasers,retrocausality, and all that was discussed. The first volume gave an introduction to teichmuller theory. Teichmuller theory is the everexpanding manual to this unique feature of mathematics. Buy teichmuller theory and applications to geometry, topology, and dynamics on. Introduction much of the theory of riemann surfaces boils down to the following theorem, the twodimensional equivalent of thurstons.
The principal 3diwensional subgroup details of the theory summarized here will be found in kostants three papers 8, 9 and 10. We begin by discussing two possible deformation spaces for pcf maps, one within rational maps, and one within the larger space of conformal dynamical systems. An introduction to teichmuller theory notes from a course given by dick canary, fall 2015 november 23, 2015 1 an overview of hyperbolic geometry 1. The arithmetic of elliptic curves and advanced topics in the arithmetic of elliptic curves by joseph silverman. Towards a modular functor from quantum higher teichmuller theory gus schrader university of california, berkeley berkeley tokyo workshop on quantum field theory and subfactors november 18, 2016 gus schrader uc berkeley quantum higher teichmuller theory berkeley tokyo workshop on quantum field theory and subfactors november 18, 2016 1 19. Chekhov held at the university of manchester in may 2006 and februarymarch 2007.
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