Weil Petersson Metric On The Universal Teichmuller Space PDF Download
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Author | : Leon Armenovich Takhtadzhi︠a︡n |
Publisher | : American Mathematical Soc. |
Total Pages | : 136 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 0821839365 |
Download Weil-Petersson Metric on the Universal Teichmuller Space Book in PDF, ePub and Kindle
In this memoir, we prove that the universal Teichmuller space $T(1)$ carries a new structure of a complex Hilbert manifold and show that the connected component of the identity of $T(1)$ -- the Hilbert submanifold $T {0 (1)$ -- is a topological group. We define a Weil-Petersson metric on $T(1)$ by Hilbert space inner products on tangent spaces, compute its Riemann curvature tensor, and show that $T(1)$ is a Kahler-Einstein manifold with negative Ricci and sectional curvatures. We introduce and compute Mumford-Miller-Morita characteristic forms for the vertical tangent bundle of the universal Teichmuller curve fibration over the universal Teichmuller space. As an application, we derive Wolpert curvature formulas for the finite-dimensional Teichmuller spaces from the formulas for the universal Teichmuller space. We study in detail the Hilbert manifold structure on $T {0 (1)$ and characterize points on $T {0 (1)$ in terms of Bers and pre-Bers embeddings by proving that the Grunsky operators $B {1 $ and The results of this memoir were presented in our e-prints: Weil-Petersson metric on the universal Teichmuller space I. Curvature properties and Chern forms, arXiv:math.CV/0312172 (2003), and Weil-Petersson metric on the universal Teichmuller space II. Kahler potential and period mapping, arXiv:math.CV/0406408 (2004).
Author | : Yoichi Imayoshi |
Publisher | : Springer Science & Business Media |
Total Pages | : 291 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 4431681744 |
Download An Introduction to Teichmüller Spaces Book in PDF, ePub and Kindle
This book offers an easy and compact access to the theory of TeichmA1/4ller spaces, starting from the most elementary aspects to the most recent developments, e.g. the role this theory plays with regard to string theory. TeichmA1/4ller spaces give parametrization of all the complex structures on a given Riemann surface. This subject is related to many different areas of mathematics including complex analysis, algebraic geometry, differential geometry, topology in two and three dimensions, Kleinian and Fuchsian groups, automorphic forms, complex dynamics, and ergodic theory. Recently, TeichmA1/4ller spaces have begun to play an important role in string theory. Imayoshi and Taniguchi have attempted to make the book as self-contained as possible. They present numerous examples and heuristic arguments in order to help the reader grasp the ideas of TeichmA1/4ller theory. The book will be an excellent source of information for graduate students and reserachers in complex analysis and algebraic geometry as well as for theoretical physicists working in quantum theory.
Author | : Arthur E. Fischer |
Publisher | : |
Total Pages | : 43 |
Release | : 1982 |
Genre | : |
ISBN | : |
Download On the Weil-Petersson metric on Teichmueller space Book in PDF, ePub and Kindle
Author | : Björn Gustafsson |
Publisher | : Springer |
Total Pages | : 329 |
Release | : 2014-11-14 |
Genre | : Science |
ISBN | : 3319082876 |
Download Classical and Stochastic Laplacian Growth Book in PDF, ePub and Kindle
This monograph covers a multitude of concepts, results, and research topics originating from a classical moving-boundary problem in two dimensions (idealized Hele-Shaw flows, or classical Laplacian growth), which has strong connections to many exciting modern developments in mathematics and theoretical physics. Of particular interest are the relations between Laplacian growth and the infinite-size limit of ensembles of random matrices with complex eigenvalues; integrable hierarchies of differential equations and their spectral curves; classical and stochastic Löwner evolution and critical phenomena in two-dimensional statistical models; weak solutions of hyperbolic partial differential equations of singular-perturbation type; and resolution of singularities for compact Riemann surfaces with anti-holomorphic involution. The book also provides an abundance of exact classical solutions, many explicit examples of dynamics by conformal mapping as well as a solid foundation of potential theory. An extensive bibliography covering over twelve decades of results and an introduction rich in historical and biographical details complement the eight main chapters of this monograph. Given its systematic and consistent notation and background results, this book provides a self-contained resource. It is accessible to a wide readership, from beginner graduate students to researchers from various fields in natural sciences and mathematics.
Author | : Jerrold E. Marsden |
Publisher | : Springer |
Total Pages | : 527 |
Release | : 2007-06-05 |
Genre | : Mathematics |
ISBN | : 3540724702 |
Download Hamiltonian Reduction by Stages Book in PDF, ePub and Kindle
This volume provides a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. It gives special emphasis to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. The volume also provides ample background theory on symplectic reduction and cotangent bundle reduction.
Author | : John Hamal Hubbard |
Publisher | : |
Total Pages | : 576 |
Release | : 2022-02 |
Genre | : |
ISBN | : 9781943863013 |
Download Teichmüller Theory and Applications to Geometry, Topology, and Dynamics Book in PDF, ePub and Kindle
Author | : Ken’ichi Ohshika |
Publisher | : Springer Nature |
Total Pages | : 456 |
Release | : |
Genre | : |
ISBN | : 3031435028 |
Download In the Tradition of Thurston III Book in PDF, ePub and Kindle
Author | : Benson Farb |
Publisher | : American Mathematical Soc. |
Total Pages | : 384 |
Release | : 2006-09-12 |
Genre | : Mathematics |
ISBN | : 0821838385 |
Download Problems on Mapping Class Groups and Related Topics Book in PDF, ePub and Kindle
The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
Author | : Katrina Barron |
Publisher | : American Mathematical Soc. |
Total Pages | : 282 |
Release | : 2017-08-15 |
Genre | : Mathematics |
ISBN | : 1470426668 |
Download Lie Algebras, Vertex Operator Algebras, and Related Topics Book in PDF, ePub and Kindle
This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.
Author | : Benson Farb |
Publisher | : American Mathematical Soc. |
Total Pages | : 371 |
Release | : 2013-08-16 |
Genre | : Mathematics |
ISBN | : 0821898876 |
Download Moduli Spaces of Riemann Surfaces Book in PDF, ePub and Kindle
Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.