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. Morrison, moduli of curves, graduate texts in math. Introduction much of the theory of riemann surfaces boils down to the following theorem, the twodimensional equivalent of thurstons. Riemann surfaces and teichmuller theory l24 stergios m. Let us quote thurston, from his foreword to hubbards book on teichmuller spaces 85. Download citation an introduction to padic teichmuller theory in this article, we survey a theory, developed by the author, concerning the uniformization of padic hyperbolic curves and their. Teichmuller theory and applications matrix editions. Theorem 5 teichmuller theorem suppose are compact riemann surfaces of genus and is a given homeomorphism. His approach to quasiconformal maps is more friendly to. It is a basic tool in the study of riemanns moduli spaces and the mapping class groups.
Thats really all you need to pick up an introduction to the subject. Inthepresentpaper,whichisthesecondinaseriesoffourpa. The hubbard model is an approximate model used, especially in solidstate physics, to describe the transition between conducting and insulating systems. 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 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. Originally, teichmuller theory was the study of moduli of complex structures on surfaces. 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 theory and applications to geometry, topology, and dynamics hardcover june 6, 2006. Teichmuller theory is the everexpanding manual to this unique feature of mathematics. Teichmuller theory and applications to geometry, topology, and dynamics. Penner there is an essentially tinkertoy model of a trivial bundle over the classical teichmuller space of a punctured surface, called the decorated teichmuller space, where the fiber over a point is the space of all tuples of horocycles, one about each puncture. Higher teichmuller theory attempts to create an analogous theory of representations of hyperbolic groups into higher rank lie groups, e. 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 and applications to geometry topology. Complex structures, jacobians and the weil petersson form 31 lecture 4. My understanding of these subjects is not very solid at this moment, but this is what i understand. Interuniversal teichmuller theory i construction of hodge theaters shinichi mochizuki may2020 abstract. Teichmuller theory and applications to geometry, topology. We assume s 0 and 2 2g s teichmuller theory volume 2. Let s be a compact oriented surface, with or without boundary. Every proof comes with geometric intuition, aided by many diagrams. May 01, 2006 buy teichmuller theory and applications to geometry, topology, and dynamics book online at best prices in india on. See, for example, kiran kedlayas lecture at the 2015 conference on interuniversal teichmuller theory at oxford. The patterson and bersgreenberg isomorphism theorems 29 2. Jost makes up for the density of the text with its clarity.
Ill indicate its broad lines in the next few paragraphs. Gardiner and nikola lakic, quasiconformal teichmuller theory, 2000 75 greg hjorth, classification and orbit equivalence relations, 2000 74 daniel w. The first volume gave an introduction to teichmuller theory. Teichmuller theory and applications to geometry, topology, and. Jan 10, 2015 the mantra is studying objects in families gives important information about the individual objects.
His approach to quasiconformal maps is more friendly to those who shy away from the hard analysis approach usually taken on the subject. 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. Teichmuller theory and applications to geometry, topology, and dynamics volume 2. John hubbard has a recent book on teichmuller theory which is quite good and geometric. This course was a prequel to the 19931994 course on thurstons hyperbolization. For general references for teichmuller theory, and quasiconformal mappings i refer to the books of l. This is the content of teichmuller theory and the main theorem is the following. It is based on a course i taught at university of utah in 19921993. Bfw16a datasheet pdf bfw16a datasheet, bfw16a circuit, bfw16a data sheet. Surface homeomorphisms and rational functions john h. So padic teichmuller theory, the padic analogue the fuchsian uniformization of teichmuller theory, is the study of integral frobenius invariant indigenous bundles. The serious mathematics in this volume is teichmuller theory, a theory of.
Siemens npn silicon rf broadband transistor,alldatasheet. Buy teichmuller theory and applications to geometry, topology. Irma lectures in mathematics and theoretical physics v, olume 19. Tugrul hakioglu may, 2005 this thesis is mainly an e. Athanase papadopoulos teichmuller theory is one of those few wonderful subjects which bring together, at an equally important level, fundamental ideas coming from different. Then there exists a unique quasiconformal map such that is homotopy equivalent to and has the smallest dilatation among all such. The fenchelnielsen coordinates so named after werner fenchel and jakob nielsen on the teichmuller space are associated to a pants decomposition of the surface.
A quick and elementary question from hubbards teichmuller. The goal of this paper is to develop an arithmetic teichmuller theory, by which we mean, introducing arithmetic objects. Stroock, an introduction to the analysis of paths on a riemannian manifold, 2000 73 john locker, spectral theory of nonselfadjoint twopoint differential operators, 2000. It was introduced and developed by shinichi mochizuki 1996, 1999 the first problem is to reformulate the fuchsian uniformization of a complex riemann surface an. Samples pages from each chapter and the appendices pdf.
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. Anabelian geometry tries to ask how much information about a variety is contained in its etale fundamental. Antonakoudis this is an introduction to the theory of conformal dynamical systems, riemann surfaces and their moduli spaces. What is a good introduction to teichmuller theory, mapping class groups etc. How are motives related to anabelian geometry and galois. Teichmuller theory mathematisches institut universitat bonn. So you would need complex analysis and probably real analysis before that. Teichmuller space encodes the possible number of ways in which you can deform complex structure on a space.
I have long held a great admiration and appreciation for john hamal hubbard and his passionate engagement with mathematics its a good book, but it builds up alot of technique before it gets to defining teichmuller teich,uller. Get your kindle here, or download a free kindle reading app. The hubbard model, named after john hubbard, is the simplest model of interacting particles in a lattice, with only two terms in the hamiltonian see example below. For a reference to the mapping class group i refer to the book of n.
A road to interuniversal teichmuller theory mathoverflow. Interuniversal teichmuller theory ii hodgearakelovtheoretic evaluation shinichi mochizuki may2020 abstract. Handbook of teichmuller theory, volume i irma lectures in mathematics and theoretical physics athanase papadopoulos download bok. Geometry of teichmuller space with the teichmuller metric. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. Its roots lie in the work of riemann and, more particularly. What are the mathematical prerequisites to understanding.
Teichmuller theory is an amazing subject, richly connected to geometry, topology, dynamics, analysis and. Handbook of teichmuller theory, volume i irma lectures in. Let g be a split semisimple algebraic group with trivial center. Complete, selfcontained treatment of teichmuller theory, providing the background needed for proving the theorems by williamthurston discussed in volume 2. 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. Teichmuller theory and applications volume 1 pdf free download. Hubbard s book is by far the most readable for the average good student i dont think fheory makes sense to thwory with anything else right now. 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. We introduce the theory for thurstons characterization for postcritically finite rational maps1. Thurston writes that john hubbard approaches mathematics with his whole mind. Teichmuller theory project that started as an attempt to present various aspects of this theory with its relations to fields, including, but not limited to, riemann surface theory, lowdimensional topology, partial differential equations, and mathematical physics. Polynomials, hubbard trees, and matings the thurston. Mochizuki, shinichi 1996, a theory of ordinary padic curves, kyoto university.
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. These objects are fundamental in several fields of mathematics, including algebraic geometry. Teichmuller theory, by jh hubbard, with american mathematical. The mantra is studying objects in families gives important information about the individual objects. Moduli spaces of local systems and higher teichmuller theory.
Theory anton zeitlin outline introduction cast of characters coordinates on superteichmuller space n 2 superteichmuller theory open problems introduction let fg s f be the riemann surface of genus g and s punctures. Teichmuller theory and applications to geometry topology and. Depending on the approach you take to teichmuller theory, some knowledge of manifolds and differential geometry would also be helpful. Introduction an orientation preserving homeomorphism ffrom a riemann surface x onto a riemann surface y is given. Polynomials, hubbard trees, and matings the thurston theory a. 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 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. Teichmuller theory and applications to geometry, topology, and dynamics volume 1. Classical teichmuller theory is a topic in complex analysis. Bers embedding and the bers boundary of teichmuller. In recoltes et semailles, grothendieck remarks that the theory of motives is related to anabelian geometry and galois teichmuller theory.
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