Quasiconformal teichmuller theory pdf merge

This volume uses quasiconformal mapping to give a unified and uptodate treatment of \tx\. By grothendiecks anabelian conjectures, galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over numberfields encode all the arithmetic information of these curves. This is dictated by the difficulty of the subject, and. Stroock, an introduction to the analysis of paths on a riemannian manifold, 2000 73 john locker, spectral theory of nonselfadjoint twopoint differential operators, 2000. Surface homeomorphisms and rational functions john h. Pdf quasiconformal maps and teichmuller theoryextremal.

There are some variations in the terminology of mapping class groups. This volume includes a wide range of papers on teichmuller theory and related areas. Schatz, teichmuller theory for surfaces with boundary, to appear. Combining all these results together we have the following theorem. Depending on the approach you take to teichmuller theory, some knowledge of manifolds and differential geometry would also be helpful.

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. Usually, the term extended mapping class group of a. Price new from used from hardcover, january 1, 2016. Introduction an orientation preserving homeomorphism ffrom a riemann surface x onto a riemann surface y is given. Quasiconformal mappings, from ptolemys geography to the. Teichmuller spaces for surfaces with cone points have come into play. Abstract we present a brief exposition of teichmullers. This is a space of equivalence classes of normalized quasiconformal. Introduction an orientation preserving homeomorphism f from a riemann surface x onto a riemann surface y is given. Then there exists a complete hyperbolic structure x with geodesic boundary on the pair of pants s2 \ 3 discs such that lengths of boundary curves are l1,l2,l3.

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 topological type defined over numberfields. An orientationpreserving mapping is called quasiconformal or a mapping with bounded distortion if. Given a quasiconformal hyperbolic surface of nite type, s, the teichmull er space modeled on s, denoted t s, is the set of equivalence classes of pairs x. Use 3 disjoint mutually nonseparating geodesics in h2 such that hyperbolic distances between them are the numbers. The theorem generalizes the riemann mapping theorem from conformal to quasiconformal homeomorphisms, and is stated as follows. This volume contains the proceedings of the ams special session on quasiconformal mappings, riemann surfaces, and teichmuller spaces, held in honor of clifford j. Quasiconformal mappings, riemann surfaces, and teichmuller. To prove the theorem, we need to be able to estimate hyperbolic lengths of simple. Another important subject is the study of the action of the action of the mapping class group on teichmuller space. 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. Based on a series of graduate lectures given by vladimir markovic at the university of warwick in spring 2003, this book is accessible to those with a grounding in complex analysis looking for an introduction to the theory of quasiconformal maps and teichmuller theory. The teichmuller space \tx\ is the space of marked conformal structures on a given quasiconformal surface \x\.

Teichmuller theory and applications to geometry, topology. The moduli space mg of the riemann surfaces of genus g is the quotient space of the teichmuller. Geometry of teichmuller space with the teichmuller metric. Introduction the harishchandra research institute hri, allahabad, india, hosted the usindia workshop. Complex structures, jacobians and the weil petersson form 31 lecture 4. F d 0 for both j d 1 and j d 2, show that the limit limt. This section gives a summary of the basics of teichmull. Interuniversal teichmuller theory i construction of hodge theaters shinichi mochizuki april2020 abstract. 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. Ra that gives a combinatorial description of the teichmuller metric. In our research we observed that the role of u qsl2 is taken by quantum superalgebra u qosp1j2. Introduction the roots of quasiconformal theory lie in geography, more precisely in the study of mappings from subsets of the sphere to the euclidean plane, and the attempts to nd the \best such mappings.

Louis funar, athanase papadopoulos and bob penner abstracts of talks norbert acampo ideal triangulations and variation of the complex structure by monodromy abstract. Kerckhoff receioed 8 december 1978 introduction teichmuller space is the space of conformal structures on a topological surface mr of genus g where two are equivalent if there is a conformal map between them which is homotopic to the identity. Teichmuller space encodes the possible number of ways in which you can deform complex structure on a space. Quasiconformal mappings, from ptolemys geography to the work of. Teichmuller theory mathematisches institut universitat bonn. 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. Advances in teichmuller theory february 4 8, 20 international erwin schr odinger institute for mathematical physics esi university of vienna, vienna organized by. Teichmuller, which are the 20thcentury founders of the theory. Riemann surfaces and teichmuller theory l24 stergios m. Lars ahlforss lectures on quasiconformal mappings, based on a course he gave at harvard university in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. Grad riemann surface algebraic geometry complex analysis differential geometry ergodic theory geometry quantum theory topology.

Newest teichmullertheory questions feed subscribe to rss. Working on my current research problem, teichmuller spaces for surfaces with cone points have come into play. Teichmullers work on quasiconformal mappings 43 references 55 1. Quasiconformal mappings, riemann surfaces, and teichmuller spaces. Instead of power series, integral representations, or algebra ic techniques, the theory relies on singular integrals, geometricmeasuretheory,andsobolevspaces. The quantum group u qg is a hopf algebra deformation of the enveloping algebra ug. Quasiconformal mappings and teichmullers theorem by bers, lipman. Teichmuller space, which give a very nice description of the space for certain rie. The reader is required to have the patience to learn several theorems in the field of real analysis.

The discussion on quasiconformal mappings in chapter 4 is very important but might be one of the most difficult parts of this volume. 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. The goal of this paper is to develop an arithmetic teichmuller theory, by which we mean. Teichmuller theory and applications to geometry, topology, and dynamics, vol. The period we consider starts with claudius ptolemy c. By m obius theorem, gand ntogether can classify all the oriented surfaces of nite type up to homeomorphism. Courant institute of mathematical sciences, new york university.

Xis a quasiconformal homeomorphism, with two such pairs deemed to be equivalent if. 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. I am a professional mathematician myself, and i doubt i could manage it even within a year. In the same way that a quasiconformal mapping turns out to be a mobius transformation even without the a priori assumption that it is a homeomorphism, a quasiconformal mapping is locally homeomorphic as soon as its coefficient of quasiconformality is sufficiently close to 1. Antonakoudis this is an introduction to the theory of conformal dynamical systems, riemann surfaces and their moduli spaces. Gardiner and jun hu winter, 2005, hri, allahabad, india.

Talk by luo feng december 27, 2010 let us denote by g. 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. Emphasis is placed on parts of the theory applicable to noncompact surfaces and to surfaces possibly of infinite analytic type. Quasiconformal maps and teichmuller theory alastair. 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. Quantum group u qg let g be a simple lie algebra over c. 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 mantra is studying objects in families gives important information about the individual objects. This barcode number lets you verify that youre getting exactly the right version or edition of a book.

Classical teichmuller theory is a topic in complex analysis. If is differentiable at the point, then the linear mapping transforms a ball of the tangent space into an ellipsoid the ratio of the. What is a good introduction to teichmuller theory, mapping class groups etc. Gardiner and nikola lakic, quasiconformal teichmuller theory, 2000 75 greg hjorth, classification and orbit equivalence relations, 2000 74 daniel w. Of central importance in the theory of quasiconformal mappings in two dimensions is the measurable riemann mapping theorem, proved by lars ahlfors and lipman bers.

We mention the works of several mathematiciansgeographers done in this period. Thats really all you need to pick up an introduction to the subject. A quasiconformal mapping class is a homotopy equivalence class. These lectures develop the theory of quasiconformal mappings from scratch, give a selfcontained treatment of the beltrami. After reading many articles, posts, communication channels, etc. Note that a 1quasiconformal map is conformal by this definition. Quasiconformal homeomorphisms and dynamics iii harvard. Along somewhat di erent lines we describe some recent important work of k. Quasiconformal mapping encyclopedia of mathematics. Since the correspondence is given by the uniformization theorem. Teichmuller theory is one of those few wonderful subjects which bring together, at an equally important. Quasiconformal mappings, from ptolemys geography to the work. Much of the theory of riemann surfaces boils down to the following theorem.

Earle, from october 23, 2010, in syracuse, new york. So you would need complex analysis and probably real analysis before that. Its fairly easy to formulate some of the definitions, a few basic results, etc. An introduction to teichmuller spaces springerlink. Fletcher and markovic also deal with universal teichmuller space. Today, teichmuller theory is a substantial area of mathematics that has inter. Hubbard author see all formats and editions hide other formats and editions. Surface homeomorphisms and rational functions hardcover january 1, 2016 by john h.