John hubbard has a recent book on teichmuller theory which is quite good and geometric. Teichmuller theory mathematisches institut universitat bonn. In 1979 his researches as described in this book, culminated in the purification program. Only when comparing them it become apparent that the three spaces, hitchin components, spaces of. I, volume 11 of irma lectures in mathematics and theoretical physics. The patterson and bersgreenberg isomorphism theorems 29 2. 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. Introduction to teichmuller theory, old and new, ii. Teichmuller theory is the everexpanding manual to this unique feature of mathematics. Free geometric topology books download ebooks online. Complex structures, jacobians and the weil petersson form 31 lecture 4.
Gardiner and nikola lakic, quasiconformal teichmuller theory, 2000 75 greg hjorth, classification and orbit equivalence relations, 2000 74 daniel w. We show that the corresponding orbits provide a canonical description of certain 2. 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. Therefore the mapping class group acts on free homotopy classes of simple closed. It is the combination of joe hubbard s practical experience as a bass player and teacher that makes his teaching method so highly effective. The teichmuller space of a surface was introduced by o. Abelian differentials is the fact that several additional structures come for free due to the translation. We assume s 0 and 2 2g s teichmuller space tf has many incarnations. Gus schrader uc berkeley quantum higher teichmuller theory berkeley tokyo workshop on quantum field theory and subfactors november 18, 2016 16 19.
Hubbard, 9780971576629, available at book depository with free teichmuller theory and applications to geometry, topology, and. For the higher dimensional theory of quasiconformal. Teichmuller theory and applications to geometry, topology, and dynamics. 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. Brief contents part i introduction to economics 1 1 the scope and method of economics 1 2 the economic problem. Theory anton zeitlin outline introduction cast of characters coordinates on super teichmuller space n 2 super teichmuller theory open problems introduction let fg s f be the riemann surface of genus g and s punctures. A measurement is an observation that results in information reduction of uncertainty about a.
Handbook of teichmuller theory, volume i irma lectures in mathematics and theoretical physics athanase papadopoulos download bok. Towards a modular functor from quantum higher teichmuller theory. This is the first and only regimen in existence that has been shown in scientific studies to reduce. 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. Schwarzian derivative and projective structures 16 8. Steve lewinson simply red hubbard the phenomenally adept bassist time out joe hubbard provides a quality of teaching that can be. Two books that are friendly to algebraic geometers are it and ab. In the case of a surface with one puncture, the fundamental group is a free. This is dictated by the difficulty of the subject, and. Part a of this volume, on the metric and analytic theory of teichmuller space, con. Di erent charts are related by subtraction free birational transformations called cluster mutations. Research statement giulio tiozzo my research focuses on dynamical systems and their relations with complex analysis, teichmuller theory, ergodic theory, probability and group theory. Stroock, an introduction to the analysis of paths on a riemannian manifold, 2000 73 john locker, spectral theory of nonselfadjoint twopoint differential operators, 2000.
The grothendieck teichmul ler conjecture states that g q dgt. Teichmuller theory and applications matrix editions. Teichmuller theory, by jh hubbard, with american mathematical. Handbook of teichm ller theory ebook download free pdf. A road to interuniversal teichmuller theory mathoverflow. Random walks on teichmuller space and the mapping class group.
Towards a modular functor from quantum higher teichmuller theory gus schrader university of california, berkeley. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. Hubbard developed various methods of achieving a reduction of the effects of drugs. What is a good introduction to teichmuller theory, mapping class groups etc. Bers embedding and the bers boundary of teichmuller. 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 teichmuller s theorem. It is a basic tool in the study of riemanns moduli spaces and the mapping class groups. Ergodic theory of teichmuller flow with respect to masurveech measure. Every proof comes with geometric intuition, aided by many diagrams.
The goal of this paper is to develop an arithmetic teichmuller theory, by which we mean, introducing arithmetic objects summarizing the arithmetic. For example, the mapping theorem is proved without ever mentioning calderon zygmund theory. Always update books hourly, if not looking, search in the book search column. This last example of the frobenius mutation and the associated core consti tuted by the. Geometry of teichmuller space with the teichmuller metric. 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.
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. So far we have defined a rogers srs whose global topology may be very complicated. The finsler geometry of the teichmuller metric request pdf. For general references for teichmuller theory, and quasiconformal mappings i refer to the books of l. Grad riemann surface algebraic geometry complex analysis differential geometry ergodic theory geometry quantum theory topology.
Introduction to teichmuller theory, old and new ems publishing. Handbook of teichmuller theory, volume i irma lectures in. Teichmuller theory and applications to geometry, topology, and dynamics volume 2. It is based on a course i taught at university of utah in 19921993. Samples pages from each chapter and the appendices pdf. Jun 04, 2015 the goal of this paper is to develop an arithmetic teichmuller theory, by which we mean, introducing arithmetic objects summarizing the arithmetic information coming from all curves of the same. There are more than 1 million books that have been enjoyed by people from all over the world. Teichmuller theory and applications volume 1 pdf free download. For a reference to the mapping class group i refer to the book of n. Theory anton zeitlin outline introduction superteichmuller. Interuniversal teichmuller theory i construction of hodge theaters shinichi mochizuki april2020 abstract. Meromorphic quadratic di erentials 18 references 27 1. By the theory of \base points at in nity we have a representation g q. How to measure anything doug hubbard expert the advisory council.
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. The results of 70, 75, 42 and 28 arose completely independently, from di. Chapter 1 l extremal mappings in amle and teichmuller theory. Higher teichmuller theory attempts to create an analogous theory of representations of hyperbolic groups into higher rank lie groups, e. A brief tour of grothendieckteichmuller theory daniel miller september 2, 2014 everything in this brief note is inspired by grothendiecks revolutionary letter gro97. Super riemann surfaces 605 1forms dual to the basis d, d 2 of vector fields. Athanase papadopoulos teichmuller theory is one of those few wonderful subjects which bring together, at an equally important level, fundamental ideas coming from different. I am a professional mathematician myself, and i doubt i could manage it even within a year. These notes were written for some expository talks on teichmuller theory, given. Teichmuller space encodes the possible number of ways in which you can deform complex structure on a space. Ron hubbard, and the golden age of science fiction. Having the correct technology complete listing of all scientology lectures and written materials with instructions on how to obtain them via torrent download free download of electronic books, lectures, course packs and more true source scientology foundation free access to a large library in word doc, pdf, text, html and mp3 formats click on the materials link at. A more algebrogeometric approach to lusztigs total positivity has been developed by fock and goncharov 17, and applied in the context of higher teichmuller theory. Hubbard, phd, mt ascp associate professor, program of clinical laboratory science department of laboratory sciences and primary care school of allied health sciences texas tech university health sciences center lubbock.
This course was a prequel to the 19931994 course on thurstons hyperbolization. We consider classical teichmuller theory and the geodesic flow on the cotangent bundle of the teichmuller space. 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. Even if this were proved, it wouldnt a priori be especially helpful if we. Scarcity and choice 25 3 demand, supply, and market equilibrium 47 4 demand and supply applications 79 part ii concepts and problems in macroeconomics 97 5 introduction to macroeconomics 97 6 measuring national output and national income 111 7 unemployment. The mantra is studying objects in families gives important information about the individual objects. An invitation to higher teichmuller theory introduction. Surface homeomorphisms and rational functions john h. Curt mcmullen regularly teaches courses on the subject and he has really nice course notes on the subject.
Gus schrader uc berkeley quantum higher teichmuller theory. Teichmuller theory and applications to geometry, topology. In any event, the basic reference for this section is j. Introduction an orientation preserving homeomorphism ffrom a riemann surface x onto a riemann surface y is given.
Ill indicate its broad lines in the next few paragraphs. A brief tour of grothendieck teichmuller theory daniel miller september 2, 2014 everything in this brief note is inspired by grothendiecks revolutionary letter gro97. The theory was made public in a series of four preprints posted in. Teichmuller theory interpretation of the decomposition of the tensor product of positive representations p p into positive representations p. Teichmuller theory is one of those few wonderful subjects which bring together. Get ebooks handbook of teichm ller theory on pdf, epub, tuebl, mobi and audiobook for free. The fenchelnielsen coordinates so named after werner fenchel and jakob nielsen on the teichmuller space are associated to a pants decomposition of the surface. Semifree finite group actions on compact manifolds, torsion in lgroups, higher diagonal approximations and skeletons of k\pi,1s, evaluating the swan finiteness obstruction for finite groups, a nonconnective delooping of algebraic k theory, the algebraic theory of torsion, equivariant moore spaces, triviality of the. Teichmuller theory and applications to geometry, topology, and dynamics volume 1.