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Holomorphic Q Classes
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Book Synopsis A Primer on Mapping Class Groups by : Benson Farb
Download or read book A Primer on Mapping Class Groups written by Benson Farb and published by Princeton University Press. This book was released on 2012 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.
Book Synopsis Foliated Bundles and Characteristic Classes by : Franz W. Kamber
Download or read book Foliated Bundles and Characteristic Classes written by Franz W. Kamber and published by Springer. This book was released on 2006-11-14 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Function Classes on the Unit Disc by : Miroslav Pavlović
Download or read book Function Classes on the Unit Disc written by Miroslav Pavlović and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-08-19 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and extended edition of a well-established monograph in function theory contains a study on various function classes on the disc, a number of new results and new or easy proofs of old but interesting theorems (for example, the Fefferman-Stein theorem on subharmonic behavior or the theorem on conjugate functions in Bergman spaces) and a full discussion on g-functions.
Book Synopsis Complex Methods for Partial Differential Equations by : Heinrich Begehr
Download or read book Complex Methods for Partial Differential Equations written by Heinrich Begehr and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of manscripts mainly originating from talks and lectures given at the Workshop on Recent Trends in Complex Methods for Par tial Differential Equations held from July 6 to 10, 1998 at the Middle East Technical University in Ankara, Turkey, sponsored by The Scientific and Tech nical Research Council of Turkey and the Middle East Technical University. This workshop is a continuation oftwo workshops from 1988 and 1993 at the In ternational Centre for Theoretical Physics in Trieste, Italy entitled Functional analytic Methods in Complex Analysis and Applications to Partial Differential Equations. Since classical complex analysis of one and several variables has a long tra dition it is of high level. But most of its basic problems are solved nowadays so that within the last few decades it has lost more and more attention. The area of complex and functional analytic methods in partial differential equations, however, is still a growing and flourishing field, in particular as these methods are not only applied. Whithin the framework of holomorphic functions but are also combined with properties of generalized analytic functions. This can be seen by the many books which recently were published in this field and also by the proceedings in this ISAAC series and the ISAAC congresses and workshops.
Book Synopsis Several Complex Variables and Complex Geometry, Part I by : Eric Bedford
Download or read book Several Complex Variables and Complex Geometry, Part I written by Eric Bedford and published by American Mathematical Soc.. This book was released on 1991 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Holomorphic Curves in Low Dimensions by : Chris Wendl
Download or read book Holomorphic Curves in Low Dimensions written by Chris Wendl and published by Springer. This book was released on 2018-06-28 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019
Book Synopsis Geometric Qp Functions by : Jie Xiao
Download or read book Geometric Qp Functions written by Jie Xiao and published by Springer Science & Business Media. This book was released on 2006-11-15 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book documents the rich structure of the holomorphic Q function spaces which are geometric in the sense that they transform naturally under conformal mappings, with particular emphasis on recent development based on interaction between geometric function and measure theory and other branches of mathematical analysis, including potential theory, harmonic analysis, functional analysis, and operator theory. Largely self-contained, the book functions as an instructional and reference work for advanced courses and research in conformal analysis, geometry, and function spaces. Self-contained, the book functions as an instructional and reference work for advanced courses and research in conformal analysis, geometry, and function spaces.
Book Synopsis Complex Algebraic Surfaces by : Arnaud Beauville
Download or read book Complex Algebraic Surfaces written by Arnaud Beauville and published by Cambridge University Press. This book was released on 1996-06-28 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch of mathematics. In this book Professor BeauviIle gives a lucid and concise account of the subject, following the strategy of F. Enriques, but expressed simply in the language of modern topology and sheaf theory, so as to be accessible to any budding geometer. This volume is self contained and the exercises succeed both in giving the flavour of the extraordinary wealth of examples in the classical subject, and in equipping the reader with most of the techniques needed for research.
Book Synopsis A Course in Complex Analysis and Riemann Surfaces by : Wilhelm Schlag
Download or read book A Course in Complex Analysis and Riemann Surfaces written by Wilhelm Schlag and published by American Mathematical Society. This book was released on 2014-08-06 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analysis is a cornerstone of mathematics, making it an essential element of any area of study in graduate mathematics. Schlag's treatment of the subject emphasizes the intuitive geometric underpinnings of elementary complex analysis that naturally lead to the theory of Riemann surfaces. The book begins with an exposition of the basic theory of holomorphic functions of one complex variable. The first two chapters constitute a fairly rapid, but comprehensive course in complex analysis. The third chapter is devoted to the study of harmonic functions on the disk and the half-plane, with an emphasis on the Dirichlet problem. Starting with the fourth chapter, the theory of Riemann surfaces is developed in some detail and with complete rigor. From the beginning, the geometric aspects are emphasized and classical topics such as elliptic functions and elliptic integrals are presented as illustrations of the abstract theory. The special role of compact Riemann surfaces is explained, and their connection with algebraic equations is established. The book concludes with three chapters devoted to three major results: the Hodge decomposition theorem, the Riemann-Roch theorem, and the uniformization theorem. These chapters present the core technical apparatus of Riemann surface theory at this level. This text is intended as a detailed, yet fast-paced intermediate introduction to those parts of the theory of one complex variable that seem most useful in other areas of mathematics, including geometric group theory, dynamics, algebraic geometry, number theory, and functional analysis. More than seventy figures serve to illustrate concepts and ideas, and the many problems at the end of each chapter give the reader ample opportunity for practice and independent study.
Book Synopsis Geometry and Topology of Manifolds by : Hans U. Boden
Download or read book Geometry and Topology of Manifolds written by Hans U. Boden and published by American Mathematical Soc.. This book was released on with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains expository papers that give an up-to-date account of recent developments and open problems in the geometry and topology of manifolds, along with several research articles that present new results appearing in published form for the first time. The unifying theme is the problem of understanding manifolds in low dimensions, notably in dimensions three and four, and the techniques include algebraic topology, surgery theory, Donaldson and Seiberg-Witten gauge theory, Heegaard Floer homology, contact and symplectic geometry, and Gromov-Witten invariants. The articles collected for this volume were contributed by participants of the Conference "Geometry and Topology of Manifolds" held at McMaster University on May 14-18, 2004 and are representative of the many excellent talks delivered at the conference.
Book Synopsis Differential Geometry, Part 1 by : Shiing-Shen Chern
Download or read book Differential Geometry, Part 1 written by Shiing-Shen Chern and published by American Mathematical Soc.. This book was released on 1975 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors by : Jan H. Bruinier
Download or read book Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors written by Jan H. Bruinier and published by Springer. This book was released on 2004-10-11 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Around 1994 R. Borcherds discovered a new type of meromorphic modular form on the orthogonal group $O(2,n)$. These "Borcherds products" have infinite product expansions analogous to the Dedekind eta-function. They arise as multiplicative liftings of elliptic modular forms on $(SL)_2(R)$. The fact that the zeros and poles of Borcherds products are explicitly given in terms of Heegner divisors makes them interesting for geometric and arithmetic applications. In the present text the Borcherds' construction is extended to Maass wave forms and is used to study the Chern classes of Heegner divisors. A converse theorem for the lifting is proved.
Book Synopsis Foliations 2005 - Proceedings Of The International Conference by : Pawel Walczak
Download or read book Foliations 2005 - Proceedings Of The International Conference written by Pawel Walczak and published by World Scientific. This book was released on 2006-09-20 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume takes a look at the current state of the theory of foliations, with surveys and research articles concerning different aspects. The focused aspects cover geometry of foliated Riemannian manifolds, Riemannian foliations and dynamical properties of foliations and some aspects of classical dynamics related to the field. Among the articles readers may find a study of foliations which admit a transverse contractive flow, an extensive survey on non-commutative geometry of Riemannian foliations, an article on contact structures converging to foliations, as well as a few articles on conformal geometry of foliations. This volume also contains a list of open problems in foliation theory which were collected from the participants of the Foliations 2005 conference.
Book Synopsis Algebraic and Geometric Aspects of Integrable Systems and Random Matrices by : Anton Dzhamay
Download or read book Algebraic and Geometric Aspects of Integrable Systems and Random Matrices written by Anton Dzhamay and published by American Mathematical Soc.. This book was released on 2013-06-26 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, held from January 6-7, 2012, in Boston, MA. The very wide range of topics represented in this volume illustrates
Book Synopsis Quantum Fields and Strings: A Course for Mathematicians by : Pierre Deligne
Download or read book Quantum Fields and Strings: A Course for Mathematicians written by Pierre Deligne and published by American Mathematical Society. This book was released on 1999-10-25 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: A run-away bestseller from the moment it hit the market in late 1999. This impressive, thick softcover offers mathematicians and mathematical physicists the opportunity to learn about the beautiful and difficult subjects of quantum field theory and string theory. Cover features an intriguing cartoon that will bring a smile to its intended audience.
Book Synopsis Cycle Spaces of Flag Domains by : Gregor Fels
Download or read book Cycle Spaces of Flag Domains written by Gregor Fels and published by Springer Science & Business Media. This book was released on 2006-07-30 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Driven by numerous examples from the complex geometric viewpoint New results presented for the first time Widely accessible, with all necessary background material provided for the nonspecialist Comparisons with classical Barlet cycle spaces are given Good bibliography and index
Book Synopsis Theory of Analytic Functions of Several Complex Variables by : Boris Abramovich Fuks
Download or read book Theory of Analytic Functions of Several Complex Variables written by Boris Abramovich Fuks and published by American Mathematical Soc.. This book was released on 1963 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:
