Handbook Of Teichm Ller Theory
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Handbook Of Teichm Ller Theory
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Author : Athanase Papadopoulos
language : en
Publisher: European Mathematical Society
Release Date : 2007
Handbook Of Teichm Ller Theory written by Athanase Papadopoulos and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.
Handbook Of Teichm Ller Theory
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Author : Athanase Papadopoulos
language : en
Publisher: European Mathematical Society
Release Date : 2007
Handbook Of Teichm Ller Theory written by Athanase Papadopoulos and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The subject of this handbook is Teichmuller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with $3$-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas toward a unique subject is a manifestation of the unity and harmony of mathematics. This volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in these fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. This volume is divided into the following four sections: The metric and the analytic theory The group theory The algebraic topology of mapping class groups and moduli spaces Teichmuller theory and mathematical physics This handbook is addressed to graduate students and researchers in all the fields mentioned.
Handbook Of Teichm Ller Theory
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Author : Athanase Papadopoulos
language : en
Publisher: European Mathematical Society
Release Date : 2007
Handbook Of Teichm Ller Theory written by Athanase Papadopoulos and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The Teichmuller space of a surface was introduced by O. Teichmuller in the 1930s. It is a basic tool in the study of Riemann's moduli spaces and the mapping class groups. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. The original setting of Teichmuller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry to the study of Teichmuller space and its asymptotic geometry. Teichmuller spaces are also studied from the point of view of the representation theory of the fundamental group of the surface in a Lie group $G$, most notably $G=\mathrm{PSL}(2,\mathbb{R})$ and $G=\mathrm{PSL}(2,\mathbb{C})$. In the 1980s, there evolved an essentially combinatorial treatment of the Teichmuller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmuller space, the Weil-Petersson symplectic and Poisson geometry of this space as well as gauge-theoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3-manifolds. The purpose of this handbook is to give a panorama of some of the most important aspects of Teichmuller theory. The handbook should be useful to specialists in the field, to graduate students, and more generally to mathematicians who want to learn about the subject. All the chapters are self-contained and have a pedagogical character. They are written by leading experts in the subject.
Handbook Of Teichm Ller Theory
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Author : Athanase Papadopoulos
language : en
Publisher:
Release Date : 2020
Handbook Of Teichm Ller Theory written by Athanase Papadopoulos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
Handbook Of Teichm Ller Theory
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Author : Athanase Papadopoulos
language : en
Publisher:
Release Date :
Handbook Of Teichm Ller Theory written by Athanase Papadopoulos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The subject of this handbook is Teichmüller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with 3-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas towards a unique subject is a manifestation of the unity and harmony of mathematics. The present volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in the fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. The metric and the analytic theory. The group theory. The algebraic topology of mapping class groups and moduli spaces. Teichmüller theory and mathematical physics. The handbook is addressed to graduate students and researchers in all the fields mentioned.
Handbook Of Teichm Ller Theory
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Author :
language : en
Publisher:
Release Date : 2014
Handbook Of Teichm Ller Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
Handbook Of The History And Philosophy Of Mathematical Practice
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Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date : 2024-04-26
Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-26 with Mathematics categories.
The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy – as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today – who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute ofTechnology, USA Jody Azzouni, Tufts University, USA Otávio Bueno, University of Miami, USA William Byers, Concordia University, Canada Carlo Cellucci, Sapienza University of Rome, Italy Chandler Davis, University of Toronto, Canada (1926-2022) Paul Ernest, University of Exeter, UK Michele Friend, George Washington University, USA Reuben Hersh, University of New Mexico, USA (1927-2020) Kyeong-Hwa Lee, Seoul National University, South Korea Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023) Athanase Papadopoulos, University of Strasbourg, France Ulf Persson, Chalmers University of Technology, Sweden John Stillwell, University of San Francisco, USA David Tall, University of Warwick, UK (1941-2024) This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin. ---Barry Mazur, Gerhard Gade University Professor, Harvard University This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate. ---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize Dedicating a volume to the memory of three mathematicians – Chandler Davis, Reuben Hersh, and Yuri Manin –, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration! ---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques
Handbook Of Homotopy Theory
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Author : Haynes Miller
language : en
Publisher:
Release Date : 2024-10-14
Handbook Of Homotopy Theory written by Haynes Miller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-14 with Mathematics categories.
The Handbook of Homotopy established the state-of-the-art research on this emerging topic in topology. The list of topics and contributors is impressive. The topics cover a broad swath, and the contributors will do an outstanding job. Students particularly will findthis book to be an entree to an active field of study.
Handbook Of Complex Analysis
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Author : Reiner Kuhnau
language : en
Publisher: Elsevier
Release Date : 2002-12-05
Handbook Of Complex Analysis written by Reiner Kuhnau and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-05 with Mathematics categories.
Geometric Function Theory is a central part of Complex Analysis (one complex variable). The Handbook of Complex Analysis - Geometric Function Theory deals with this field and its many ramifications and relations to other areas of mathematics and physics. The theory of conformal and quasiconformal mappings plays a central role in this Handbook, for example a priori-estimates for these mappings which arise from solving extremal problems, and constructive methods are considered. As a new field the theory of circle packings which goes back to P. Koebe is included. The Handbook should be useful for experts as well as for mathematicians working in other areas, as well as for physicists and engineers.· A collection of independent survey articles in the field of GeometricFunction Theory · Existence theorems and qualitative properties of conformal and quasiconformal mappings · A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane)
The Geometric Theory Of Complex Variables
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Author : Peter V. Dovbush
language : en
Publisher: Springer Nature
Release Date : 2025-01-28
The Geometric Theory Of Complex Variables written by Peter V. Dovbush and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-28 with Mathematics categories.
This book provides the reader with a broad introduction to the geometric methodology in complex analysis. It covers both single and several complex variables, creating a dialogue between the two viewpoints. Regarded as one of the 'grand old ladies' of modern mathematics, complex analysis traces its roots back 500 years. The subject began to flourish with Carl Friedrich Gauss's thesis around 1800. The geometric aspects of the theory can be traced back to the Riemann mapping theorem around 1850, with a significant milestone achieved in 1938 with Lars Ahlfors's geometrization of complex analysis. These ideas inspired many other mathematicians to adopt this perspective, leading to the proliferation of geometric theory of complex variables in various directions, including Riemann surfaces, Teichmüller theory, complex manifolds, extremal problems, and many others. This book explores all these areas, with classical geometric function theory as its main focus. Its accessible and gentle approach makes it suitable for advanced undergraduate and graduate students seeking to understand the connections among topics usually scattered across numerous textbooks, as well as experienced mathematicians with an interest in this rich field.