Tugrul hakioglu may, 2005 this thesis is mainly an e. Schatz, teichmuller theory for surfaces with boundary, to appear. The mantra is studying objects in families gives important information about the individual objects. Much of this theory can be expressed in the language of anosov representations, which appear to be the correct generalization of the notion of a convex cocompact representation into a rank one lie. Nov 10, 2003 let g be a split semisimple algebraic group with trivial center. It is based on a course i taught at university of utah in 19921993. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. Part a of this volume, on the metric and analytic theory of teichmuller space, con. Thats really all you need to pick up an introduction to the subject. Athanase papadopoulos teichmuller theory is one of those few wonderful subjects which bring together, at an equally important level, fundamental ideas coming from different. 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.
Howard alan masur is an american mathematician who works on topology, geometry and combinatorial group theory. We remark that there is a large literature on teichmuller theory, some of which has bearing. Interaction with analysis, geometry and number theory from 4 to 16 july, 2011. An invitation to higher teichmuller theory introduction.
Only when comparing them it become apparent that the three spaces, hitchin components, spaces of. Higher teichmuller theory attempts to create an analogous theory of representations of hyperbolic groups into higher rank lie groups, e. Raction on these moduli spaces, the kontsevichzorich cocycle over the teichmuller geodesic. What is a good introduction to teichmuller theory, mapping class groups etc. Handbook of teichm ller theory ebook download free pdf. Surface homeomorphisms and rational functions john h. So you would need complex analysis and probably real analysis before that. Teichmuller space encodes the possible number of ways in. Teichmuller theory is one of those few wonderful subjects which bring. The hubbardmasur theorem is named after masur and john h. 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. Let g be a split semisimple algebraic group with trivial center. Printed in great britain the asymptotic geometry of teichmuller space steven p. Teichmuller spaces of riemann surfaces, moduli spaces and modular groups.
Every proof comes with geometric intuition, aided by many diagrams. Samples pages from each chapter and the appendices pdf. Teichmuller theory mathematisches institut universitat bonn. In any event, the basic reference for this section is j. The results of 70, 75, 42 and 28 arose completely independently, from di.
The grothendieck teichmuller theory dessins denfants, grothendiecks reconstruction principle, and the teichmuller theory of the solenoid. Teichmuller theory and applications to geometry, topology, and dynamics volume 2. Teichmuller theory is the everexpanding manual to this unique feature of mathematics. We define \\it positive representations of the fundamental group of s to gr, construct explicitly all positive representations, and prove that they are faithful, discrete, and positive hyperbolic. For example, the mapping theorem is proved without ever mentioning calderon zygmund theory. Teichmuller theory the teichmuller space of a riemann surface is the space of all deformations of the complex structure, with a topological marking that insures that the teichmuller space is simply connected. Bers embedding and the bers boundary of teichmuller. Ill indicate its broad lines in the next few paragraphs. There are moreover many survey articles on various aspects of the theory, no tably the articles in the recent handbook of teichmuller theory, vol.
Teichmuller theory and applications to geometry, topology, and dynamics volume 1. 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. In the theory, the schwarzian derivative plays an important role. An introduction to teichmuller spaces springerlink.
This last example of the frobenius mutation and the associated core consti tuted by the. Jul 20, 2019 hubbard teichmuller theory pdf i am a music teacher. Introduction to teichmuller theory, old and new, ii. The theory was made public in a series of four preprints posted in. Interuniversal teichmuller theory i construction of hodge theaters shinichi mochizuki april2020 abstract.
Interuniversal teichmuller theory abbreviated as iut is the name given by mathematician shinichi mochizuki to a theory he developed in the 2000s, following his earlier work in arithmetic geometry. Let s be a compact oriented surface, with or without boundary. Geometry of teichmuller space with the teichmuller metric. Introduction to teichmuller theory, old and new ems publishing.
According to mochizuki, it is an arithmetic version of teichmuller theory for number fields equipped with an elliptic curve. 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. John hubbard has a recent book on teichmuller theory which is quite good and. Handbook of teichmuller theory, volume i irma lectures in mathematics and theoretical physics. For general references for teichmuller theory, and quasiconformal mappings i refer to the books of l. Handbook of teichmuller theory, volume i irma lectures in. Towards a modular functor from quantum higher teichmuller theory. I doubt there is anyone who could learn this material given anything less than a year of solid study and i am thinking of the leading researchers in the world, who are already experts in everything related.
Classical teichmuller theory is a topic in complex analysis. Moduli of riemann surfaces, teichmuller theory see also 14h15, 30fxx 58d17. English 2006 teichmuller theory and applications to geometry, topology, and. Try the kindle edition and experience these great reading features. Introduction an orientation preserving homeomorphism ffrom a riemann surface x onto a riemann surface y is given. Moduli spaces of local systems and higher teichmuller theory. For example, earlier work of hubbard, schleicher and shishikura 6 also. Depending on the approach you take to teichmuller theory, some knowledge of manifolds and differential geometry would also be helpful. Volume 1 of teichmuller theory has been a joy to read. The grothendieckteichmuller theory dessins denfants, grothendiecks reconstruction principle, and the teichmuller theory of the solenoid. 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. Two books that are friendly to algebraic geometers are it and ab.
Teichmuller theory interpretation of the decomposition of the tensor product of positive representations p p into positive representations p. Teichmuller theory and applications to geometry, topology. Teichmuller space encodes the possible number of ways in which you can deform complex structure on a space. You can also listen to your mp3 at any time in your digital library. Curt mcmullen regularly teaches courses on the subject and he has really nice course notes on the subject. Teichmuller theory and applications matrix editions.
The finsler geometry of the teichmuller metric request pdf. A road to interuniversal teichmuller theory mathoverflow. The asymptotic geometry of teichmuller space sciencedirect. For a reference to the mapping class group i refer to the book of n. This course was a prequel to the 19931994 course on thurstons hyperbolization. It is a basic tool in the study of riemanns moduli spaces and the mapping class groups. Teichmuller theory and applications volume 1 pdf free download. Hubbard teichmuller theory pdf vector calculus, linear algebra, and differential forms, a unified approach with barbara burke hubbard. Ergodic theory of teichmuller flow with respect to masurveech measure.
The teichmuller space of a surface was introduced by o. The fenchelnielsen coordinates so named after werner fenchel and jakob nielsen on the teichmuller space are associated to a pants decomposition of the surface. The patterson and bersgreenberg isomorphism theorems 29 2. Gus schrader uc berkeley quantum higher teichmuller theory berkeley tokyo workshop on quantum field theory and subfactors november 18, 2016 16 19. This handbook is an essential reference for graduate students and researchers interested in teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry. Harers lecture notes on the cohomology of moduli spaces doesnt have all the. Upon finishing his degree at the school of the art institute of chicago, he is offered a job teaching english. His approach to quasiconformal maps is more friendly to those who shy away from the hard analysis approach usually taken on the subject. Introduction much of the theory of riemann surfaces boils down to the following theorem, the twodimensional equivalent of thurstons. Complex structures, jacobians and the weil petersson form 31 lecture 4. In this survey, we give an expository account of the universal teichmuller. Jun 17, 2019 hubbard teichmuller theory pdf vector calculus, linear algebra, and differential forms, a unified approach with barbara burke hubbard.
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