Higher teichmuller theory attempts to create an analogous theory of representations of hyperbolic groups into higher rank lie groups, e. For general references for teichmuller theory, and quasiconformal mappings i refer to the books of l. Thurstons pullback map on the augmented teichmuller space and. The results of 70, 75, 42 and 28 arose completely independently, from di.
Classical teichmuller theory is a topic in complex analysis. According to mochizuki, it is an arithmetic version of teichmuller theory for number fields equipped with an elliptic curve. Curt mcmullen regularly teaches courses on the subject and he has really nice course notes on the subject. This course was a prequel to the 19931994 course on thurstons hyperbolization.
Teichmuller theory and applications to geometry, topology. So you would need complex analysis and probably real analysis before that. Teichmuller theory interpretation of the decomposition of the tensor product of positive representations p p into positive representations p. Teichmuller theory and applications matrix editions. Equations algebriques, traitement du signal et geometrie effective with florence hubert. Its connections with many aspects of geometry, topology and dynamics are actively leading to new insights and advances both within teichmuller theory and among its allied areas. Gus schrader uc berkeley quantum higher teichmuller theory berkeley tokyo workshop on quantum field theory and subfactors november 18, 2016 16 19. Handbook of teichmuller theory, volume i irma lectures in. Bers embedding and the bers boundary of teichmuller. 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 goal of this paper is to develop an arithmetic teichmuller theory, by which we mean, introducing arithmetic objects summarizing the arithmetic. Superteichmuller theory anton zeitlin outline introduction cast of characters coordinates on superteichmuller space n 2 superteichmuller theory open problems penners work in the 1980s. Teichmuller theory and applications to geometry, topology, and dynamics hardcover june 6, 2006. Teichmuller theory and applications to geometry, topology, and.
Teichmuller theory and applications to geometry, topology, and dynamics volume 1. Raction on these moduli spaces, the kontsevichzorich cocycle over the teichmuller geodesic. In mathematics, the teichmuller space t s \displaystyle ts \displaystyle ts of a real. It is based on a course i taught at university of utah in 19921993. Handbook of teichmuller theory, volume i irma lectures in mathematics and theoretical physics athanase papadopoulos download bok.
Schatz, teichmuller theory for surfaces with boundary, to appear. Introduction an orientation preserving homeomorphism ffrom a riemann surface x onto a riemann surface y is given. The theory of uniformization of \p\adic hyperbolic curves and their moduli was initiated in a previous work by mochizuki. Hubbard author see all formats and editions hide other formats and editions.
Price new from used from hardcover, january 1, 2016. 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. The patterson and bersgreenberg isomorphism theorems 29 2. Two books that are friendly to algebraic geometers are it and ab. The theory continues to be active, with numerous studies of the complex structure of teichmuller space. How to measure anything doug hubbard expert the advisory council. I read a little bit on kashaevs or chekhov and focks, but find that i need to fill.
With contributions by adrien douady, william dunbar. 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. The theory was made public in a series of four preprints posted in. John hamal hubbard oktober 1945 ist ein usamerikanischer mathematiker. Teichmuller theory and applications volume 1 pdf free download. 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. His approach to quasiconformal maps is more friendly to.
Gardiner and nikola lakic, quasiconformal teichmuller theory, 2000 75 greg hjorth, classification and orbit equivalence relations, 2000 74 daniel w. Teichmuller theory there are many good references for teichmuller theory. Grad riemann surface algebraic geometry complex analysis differential geometry ergodic theory geometry quantum theory topology. Teichmuller theory and applications to geometry, topology, and dynamics, volume i. I would like to ask for some detailed reference for quantum teichmuller theory, better in a mathematical taste. Teichmuller theory is the everexpanding manual to this unique feature of mathematics. His approach to quasiconformal maps is more friendly to those who shy away from the hard analysis approach usually taken on the subject.
Interaction with analysis, geometry and number theory from 4 to 16 july, 2011. Ill indicate its broad lines in the next few paragraphs. 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. The third, by hubbard, illustrates the role of these mappings in thurstons theory of. Introduction much of the theory of riemann surfaces boils down to the following theorem, the twodimensional equivalent of thurstons. It is a basic tool in the study of riemanns moduli spaces and the mapping class groups. 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. Every proof comes with geometric intuition, aided by many diagrams.
The serious mathematics in this volume is teichmuller theory, a theory of riemann. Depending on the approach you take to teichmuller theory, some knowledge of manifolds and differential geometry would also be helpful. Ergodic theory of teichmuller flow with respect to masurveech measure. In any event, the basic reference for this section is j. Pdf anabelian geometry, the geometry of categories 1 the profinite grothendieck conjecture for closed. A measurement is an observation that results in information reduction of uncertainty about a. The mantra is studying objects in families gives important information about the individual objects. We introduce the theory for thurstons characterization for postcritically finite rational maps1. Samples pages from each chapter and the appendices pdf.
Thats really all you need to pick up an introduction to the subject. Polynomials, hubbard trees, and matings the thurston. From its classical roots in complex analysis in the early twentieth century, teichmuller theory has become deeply embedded in the structure of modern mathematics. In the theory, the schwarzian derivative plays an important role. I am a professional mathematician myself, and i doubt i could manage it even within a year. For a reference to the mapping class group i refer to the book of n. Towards a modular functor from quantum higher teichmuller theory.
Teichmuller space encodes the possible number of ways in which you can deform complex structure on a space. Introduction to teichm\ uller theory and its applications to dynamics. 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. This is dictated by the difficulty of the subject, and. While volume 2 of hubbards book is mainly about applications to. Anton zeitlin outline introduction superteichmuller theory. Only when comparing them it become apparent that the three spaces, hitchin components, spaces of.
Teichmuller theory and applications to geometry, topology, and dynamics. What is a good introduction to teichmuller theory, mapping class groups etc. Surface homeomorphisms and rational functions hardcover january 1, 2016 by john h. Y 1 2 inf f lnk where k is the dilatation of a quasiconformal map f. Geometry of teichmuller space with the teichmuller metric. Pass one of the other snap hooks yamaaha rear view mirrors of kanual cable through the helmet the rear view mirrors of this vehicle can strap buckle, and then clip the be folded forward or backward for park snap hook onto the.
Little things acoustic verse 1 g your hand fits in mine g like its made just for me c but bear this in mind c it was meant to be em and im joining up the dots d with the freckles on. Hubbard teichmuller theory pdf vector calculus, linear algebra, and differential forms, a unified approach with barbara burke hubbard. Complex structures, jacobians and the weil petersson form 31 lecture 4. Boundary values of the thurston pullback map american. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. The hamiltonian of the hubbard model consists of two pieces. 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. The hubbard model is a highly oversimplified model for electrons in a solid which interact with each other through extremely short ranged repulsive coulomb interaction. 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.
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