For a reference to the mapping class group i refer to the book of n. In the appendix we use projective surfaces to show the closure of quasifuchsian space is not a topological manifold. The patterson and bersgreenberg isomorphism theorems 29 2. Higher teichmuller theory attempts to create an analogous theory of representations of hyperbolic groups into higher rank lie groups, e. The second of four volumes devoted to teichmuller theory and its applications to geometry, topology, and dynamics, this volume proves two theorems by william thurston. Introduction an orientation preserving homeomorphism ffrom a riemann surface x onto a riemann surface y is given. Spaces and dual geometric gibbs type measure theory for circle dyanamics yunping jiang 4435 stable maps into the classifying space of the general linear group ivan kausz 437449 limit points of iterated function systems linda keen and nikola. This ts the picture of a deformation theory for geometric structures of. Teichmuller theory and applications to geometry, topology. The theory of uniformization of \p\adic hyperbolic curves and their moduli was initiated in a previous work by mochizuki. Handbook of teichmuller theory, volume i irma lectures in.
Teichmuller theory and applications to geometry, topology, and. Bers embedding and the bers boundary of teichmuller. Pdf 3 the intrinsic hodge theory of padic hyperbolic curves nara 1998. In any event, the basic reference for this section is j.
Thats really all you need to pick up an introduction to the subject. I would like to ask for some detailed reference for quantum teichmuller theory, better in a mathematical taste. The results of 70, 75, 42 and 28 arose completely independently, from di. His approach to quasiconformal maps is more friendly to those who shy away from the hard analysis approach usually taken on the subject. Pdf comments new 20110715 2 foundations of padic teichmuller theory. In our research we observed that the role of u qsl2 is taken by quantum superalgebra u qosp1j2. What links here related changes upload file special pages permanent link page. 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. Miller cornell university march 2, 2008 abstract we provide a selfcontained, accessible introduction to ratners equidistribution theorem in the special case of horocyclic. It is a basic tool in the study of riemanns moduli spaces and the mapping class groups. Feb 11, 2015 pdf in this paper, we prove that the singular set of a harmonic map from a smooth riemannian domain to the weilpetersson completion of teichmuller. 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.
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. Jan 10, 2015 the mantra is studying objects in families gives important information about the individual objects. Masur, quadratic differentials and foliations, acta. Teichmuller theory and applications to geometry, topology, and dynamics volume i. The asymptotic geometry of teichmuller space sciencedirect. Raction on these moduli spaces, the kontsevichzorich cocycle over the teichmuller geodesic. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics.
Ill indicate its broad lines in the next few paragraphs. 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. Hubbard teichmuller theory pdf vector calculus, linear algebra, and differential forms, a unified approach with barbara burke hubbard. 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. It is based on a course i taught at university of utah in 19921993. Its dual can be identi ed with the quotient banach space l1dnd. Teichmuller space encodes the possible number of ways in which you can deform complex structure on a space. Pdf padic teichmuller theory 1 a theory of ordinary padic curves.
In mathematics, the teichmuller space t s \displaystyle ts \displaystyle t s of a real. Handbook of teichmuller theory, volume i irma lectures in mathematics and theoretical physics. Pdf quasiconformal maps and teichmuller theoryextremal. Teichmuller theory and applications matrix editions. Moduli of riemann surfaces, teichmuller theory see also 14h15, 30fxx 58d17. Interaction with analysis, geometry and number theory from 4 to 16 july, 2011. The fenchelnielsen coordinates so named after werner fenchel and jakob nielsen on the teichmuller space are associated to a pants decomposition of the surface. 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 which is homotopic to.
An introduction to teichmuller spaces springerlink. For general references for teichmuller theory, and quasiconformal mappings i refer to the books of l. He has also published the first two volumes of a book on teichmuller theory and its applications to. Let us consider two riemann surface structures s 0 and s 1 on a xed topological compact surface of genus g 1. John hamal hubbard is an american mathematician and professor at cornell university and. Thurstons pullback map on the augmented teichmuller space and. 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. Every proof comes with geometric intuition, aided by many diagrams.
Introduction much of the theory of riemann surfaces boils down to the following theorem, the twodimensional equivalent of thurstons. This paper extends the decorated teichmuller theory developed. Complex structures, jacobians and the weil petersson form 31 lecture 4. Ergodic theory of teichmuller flow with respect to masurveech measure. Athanase papadopoulos teichmuller theory is one of those few wonderful subjects which bring together, at an equally important level, fundamental ideas coming from different. Some aspects of the classical teichmulller theory a structure theorem for geodesic currents higher teichmulller theory and applications joint with m. 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. Comments new 20180403 3 an introduction to padic teichmuller theory. Samples pages from each chapter and the appendices pdf. On the verification and further development of interuniversal teichmuller theory ivan fesenko 2015, arithmetic deformation theory via arithmetic fundamental. Classical teichmuller theory is a topic in complex analysis. Surface homeomorphisms and rational functions john h. The third, by hubbard, illustrates the role of these mappings in thurstons. Teichmuller spaces and their complex and real geodesics in the intrinsic teichmuller kobayashi metric.
The kleinmaskit combination theorems john hubbard 395412 function models for teichmuller. I read a little bit on kashaevs or chekhov and focks, but find that i need to fill. The book is aimed at readers who have completed at least a year of graduate school, in conformity with the advanced level of the material. Handbook of teichmuller theory athanase papadopoulos.
Z z m y1 i1 dc id c ijfcj2 det1 zcyzc where the space mis a fundamental domain of the universal teichmuller space t1. Only when comparing them it become apparent that the three spaces, hitchin components, spaces of. 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. So you would need complex analysis and probably real analysis before that. The theory was made public in a series of four preprints posted in. Teichmuller theory and applications to geometry, topology, and dynamics. Papers of shinichi mochizuki research institute for. Equidistribution of horocyclic flows on complete hyperbolic surfaces of finite area john h. Teichmuller theory and applications to geometry, topology, and dynamics hardcover june 6, 2006. In the context of teichmuller theory, the elements of l1d are called the beltrami di erentials on d.
Teichmuller theory and applications to geometry, topology, and dynamics volume 1. 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. Printed in great britain the asymptotic geometry of teichmuller space steven p. Mcshane identities for higher teichmuller theory and the. Mochizuki rims, kyoto university interuniversal teichm. Teichmuller theory and applications volume 1 pdf free download. What is a good introduction to teichmuller theory, mapping class groups etc.
In mathematics, the teichmuller space t s \displaystyle ts \displaystyle ts of a real. 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. 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. The theory continues to be active, with numerous studies of the complex structure of teichmuller space. Nov 10, 2003 let g be a split semisimple algebraic group with trivial center. Y 1 2 inf f lnk where k is the dilatation of a quasiconformal map f. The teichmuller space of a surface was introduced by o. Induced upon each level surface of t is a riemannian metric gt the. Depending on the approach you take to teichmuller theory, some knowledge of manifolds and differential geometry would also be helpful. Historical development of teichmuller theory springerlink. The geometry of the universal teichmuller space and the. After reading many articles, posts, communication channels, etc.
Geometry of teichmuller space with the teichmuller metric. Using complex earthquakes, we prove grafting is a homeomorphism for all 1dimensional teichmuller spaces, and we construct bending coordinates on bers slices and their generalizations. Teichmuller theory is the everexpanding manual to this unique feature of mathematics. Moduli spaces of local systems and higher teichmuller theory. Grad riemann surface algebraic geometry complex analysis differential geometry ergodic theory geometry quantum theory topology. According to mochizuki, it is an arithmetic version of teichmuller theory for number fields equipped with an elliptic curve. An invitation to higher teichmuller theory introduction. In the theory, the schwarzian derivative plays an important role. In this survey, we give an expository account of the universal teichmuller. Motivated by the fact that the universal teichmuller space t1 contains all of the previous teichmu ller spaces, hong and rajeev proposed the following exact closed bosonic string theory. This course was a prequel to the 19931994 course on thurston s hyperbolization theorem which later became a book k. 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. For my own purposes the hubbard book is what id consider a natural starting point. Preliminaries in teichm uller theory teichmuller space.
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