A Course On Holomorphic Discs

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A Course on Holomorphic Discs

Author : Hansjörg Geiges
Publisher : Springer Nature
ISBN 13 : 3031360648
Total Pages : 203 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis A Course on Holomorphic Discs by : Hansjörg Geiges

Download or read book A Course on Holomorphic Discs written by Hansjörg Geiges and published by Springer Nature. This book was released on 2023-08-07 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook, based on a one-semester course taught several times by the authors, provides a self-contained, comprehensive yet concise introduction to the theory of pseudoholomorphic curves. Gromov’s nonsqueezing theorem in symplectic topology is taken as a motivating example, and a complete proof using pseudoholomorphic discs is presented. A sketch of the proof is discussed in the first chapter, with succeeding chapters guiding the reader through the details of the mathematical methods required to establish compactness, regularity, and transversality results. Concrete examples illustrate many of the more complicated concepts, and well over 100 exercises are distributed throughout the text. This approach helps the reader to gain a thorough understanding of the powerful analytical tools needed for the study of more advanced topics in symplectic topology. /divThis text can be used as the basis for a graduate course, and it is also immensely suitable for independent study. Prerequisites include complex analysis, differential topology, and basic linear functional analysis; no prior knowledge of symplectic geometry is assumed. This book is also part of the Virtual Series on Symplectic Geometry.

A Course in Complex Analysis

Author : Saeed Zakeri
Publisher : Princeton University Press
ISBN 13 : 0691207585
Total Pages : 442 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis A Course in Complex Analysis by : Saeed Zakeri

Download or read book A Course in Complex Analysis written by Saeed Zakeri and published by Princeton University Press. This book was released on 2021-11-02 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This textbook is intended for a year-long graduate course on complex analysis, a branch of mathematical analysis that has broad applications, particularly in physics, engineering, and applied mathematics. Based on nearly twenty years of classroom lectures, the book is accessible enough for independent study, while the rigorous approach will appeal to more experienced readers and scholars, propelling further research in this field. While other graduate-level complex analysis textbooks do exist, Zakeri takes a distinctive approach by highlighting the geometric properties and topological underpinnings of this area. Zakeri includes more than three hundred and fifty problems, with problem sets at the end of each chapter, along with additional solved examples. Background knowledge of undergraduate analysis and topology is needed, but the thoughtful examples are accessible to beginning graduate students and advanced undergraduates. At the same time, the book has sufficient depth for advanced readers to enhance their own research. The textbook is well-written, clearly illustrated, and peppered with historical information, making it approachable without sacrificing rigor. It is poised to be a valuable textbook for graduate students, filling a needed gap by way of its level and unique approach"--

Holomorphic Curves in Low Dimensions

Author : Chris Wendl
Publisher : Springer
ISBN 13 : 3319913719
Total Pages : 303 pages
Book Rating : 4.3/5 (199 download)

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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

Singularities and Self-intersections of Holomorphic Discs

Author : Kai Zehmisch
Publisher :
ISBN 13 :
Total Pages : 276 pages
Book Rating : 4.:/5 (56 download)

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Book Synopsis Singularities and Self-intersections of Holomorphic Discs by : Kai Zehmisch

Download or read book Singularities and Self-intersections of Holomorphic Discs written by Kai Zehmisch and published by . This book was released on 2009 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Holomorphic Discs with Dense Images

Author : Franc Forstnerič
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (254 download)

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Book Synopsis Holomorphic Discs with Dense Images by : Franc Forstnerič

Download or read book Holomorphic Discs with Dense Images written by Franc Forstnerič and published by . This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

J-holomorphic Curves and Symplectic Topology

Author : Dusa McDuff
Publisher : American Mathematical Soc.
ISBN 13 : 0821887467
Total Pages : 744 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis J-holomorphic Curves and Symplectic Topology by : Dusa McDuff

Download or read book J-holomorphic Curves and Symplectic Topology written by Dusa McDuff and published by American Mathematical Soc.. This book was released on 2012 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this book is to establish the fundamental theorems of the subject in full and rigourous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associatively of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology.

Proper Holomorphic Discs in C2

Author : Franc Forstnerič
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (487 download)

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Book Synopsis Proper Holomorphic Discs in C2 by : Franc Forstnerič

Download or read book Proper Holomorphic Discs in C2 written by Franc Forstnerič and published by . This book was released on 2001 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Holomorphic Discs in the Space of Oriented Lines Via Mean Curvature Flow and Applications

Author : Wilhelm Klingenberg
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (837 download)

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Book Synopsis Holomorphic Discs in the Space of Oriented Lines Via Mean Curvature Flow and Applications by : Wilhelm Klingenberg

Download or read book Holomorphic Discs in the Space of Oriented Lines Via Mean Curvature Flow and Applications written by Wilhelm Klingenberg and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

$J$-Holomorphic Curves and Quantum Cohomology

Author : Dusa McDuff
Publisher : American Mathematical Soc.
ISBN 13 : 0821803328
Total Pages : 220 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis $J$-Holomorphic Curves and Quantum Cohomology by : Dusa McDuff

Download or read book $J$-Holomorphic Curves and Quantum Cohomology written by Dusa McDuff and published by American Mathematical Soc.. This book was released on 1994 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: J -holomorphic curves revolutionized the study of symplectic geometry when Gromov first introduced them in 1985. Through quantum cohomology, these curves are now linked to many of the most exciting new ideas in mathematical physics. This book presents the first coherent and full account of the theory of J -holomorphic curves, the details of which are presently scattered in various research papers. The first half of the book is an expository account of the field, explaining the main technical aspects. McDuff and Salamon give complete proofs of Gromov's compactness theorem for spheres and of the existence of the Gromov-Witten invariants. The second half of the book focuses on the definition of quantum cohomology. The authors establish that the quantum multiplication exists and is associative on appropriate manifolds. They then describe the Givental-Kim calculation of the quantum cohomology of flag manifolds, leading to quantum Chern classes and Witten's calculation for Grassmanians, which relates to the Verlinde algebra. The Dubrovin connection, Gromov-Witten potential on quantum cohomology, and curve counting formulas are also discussed.

Embedding Holomorphic Discs Through Discrete Sets

Author : Franc Forstnerič
Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (164 download)

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Book Synopsis Embedding Holomorphic Discs Through Discrete Sets by : Franc Forstnerič

Download or read book Embedding Holomorphic Discs Through Discrete Sets written by Franc Forstnerič and published by . This book was released on 1995 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Course In Analysis, A - Vol V: Functional Analysis, Some Operator Theory, Theory Of Distributions

Author : Niels Jacob
Publisher : World Scientific
ISBN 13 : 9811215510
Total Pages : 854 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Course In Analysis, A - Vol V: Functional Analysis, Some Operator Theory, Theory Of Distributions by : Niels Jacob

Download or read book Course In Analysis, A - Vol V: Functional Analysis, Some Operator Theory, Theory Of Distributions written by Niels Jacob and published by World Scientific. This book was released on 2020-01-22 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an advanced textbook and a reference text in functional analysis in the wide sense. It provides advanced undergraduate and graduate students with a coherent introduction to the field, i.e. the basic principles, and leads them to more demanding topics such as the spectral theorem, Choquet theory, interpolation theory, analysis of operator semigroups, Hilbert-Schmidt operators and Hille-Tamarkin operators, topological vector spaces and distribution theory, fundamental solutions, or the Schwartz kernel theorem.All topics are treated in great detail and the text provided is suitable for self-studying the subject. This is enhanced by more than 270 problems solved in detail. At the same time the book is a reference text for any working mathematician needing results from functional analysis, operator theory or the theory of distributions.Embedded as Volume V in the Course of Analysis, readers will have a self-contained treatment of a key area in modern mathematics. A detailed list of references invites to further studies.

Fukaya Categories and Picard-Lefschetz Theory

Author : Paul Seidel
Publisher : European Mathematical Society
ISBN 13 : 9783037190630
Total Pages : 340 pages
Book Rating : 4.1/5 (96 download)

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Book Synopsis Fukaya Categories and Picard-Lefschetz Theory by : Paul Seidel

Download or read book Fukaya Categories and Picard-Lefschetz Theory written by Paul Seidel and published by European Mathematical Society. This book was released on 2008 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central objects in the book are Lagrangian submanifolds and their invariants, such as Floer homology and its multiplicative structures, which together constitute the Fukaya category. The relevant aspects of pseudo-holomorphic curve theory are covered in some detail, and there is also a self-contained account of the necessary homological algebra. Generally, the emphasis is on simplicity rather than generality. The last part discusses applications to Lefschetz fibrations and contains many previously unpublished results. The book will be of interest to graduate students and researchers in symplectic geometry and mirror symmetry.

Quantum Fields and Strings: A Course for Mathematicians

Author : Pierre Deligne
Publisher : American Mathematical Society
ISBN 13 : 0821820125
Total Pages : 747 pages
Book Rating : 4.8/5 (218 download)

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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 2000-04-27 with total page 747 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.

Different Faces of Geometry

Author : Simon Donaldson
Publisher : Springer Science & Business Media
ISBN 13 : 030648658X
Total Pages : 424 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Different Faces of Geometry by : Simon Donaldson

Download or read book Different Faces of Geometry written by Simon Donaldson and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Different Faces of Geometry - edited by the world renowned geometers S. Donaldson, Ya. Eliashberg, and M. Gromov - presents the current state, new results, original ideas and open questions from the following important topics in modern geometry: These apparently diverse topics have a common feature in that they are all areas of exciting current activity. The Editors have attracted an impressive array of leading specialists to author chapters for this volume: G. Mikhalkin (USA-Canada-Russia), V.D. Milman (Israel) and A.A. Giannopoulos (Greece), C. LeBrun (USA), Ko Honda (USA), P. Ozsvath (USA) and Z. Szabo (USA), C. Simpson (France), D. Joyce (UK) and P. Seidel (USA), and S. Bauer (Germany). One can distinguish various themes running through the different contributions. There is some emphasis on invariants defined by elliptic equations and their applications in low-dimensional topology, symplectic and contact geometry (Bauer, Seidel, Ozsvath and Szabo). These ideas enter, more tangentially, in the articles of Joyce, Honda and LeBrun.Here and elsewhere, as well as explaining the rapid advances that have been made, the articles convey a wonderful sense of the vast areas lying beyond our current understanding. Simpson's article emphasizes the need for interesting new constructions (in that case of Kahler and algebraic manifolds), a point which is also made by Bauer in the context of 4-manifolds and the 11/8 conjecture. LeBrun's article gives another perspective on 4-manifold theory, via Riemannian geometry, and the challenging open questions involving the geometry of even well-known 4-manifolds. There are also striking contrasts between the articles. The authors have taken different approaches: for example, the thoughtful essay of Simpson, the new research results of LeBrun and the thorough expositions with homework problems of Honda. One can also ponder the differences in the style of mathematics. In the articles of Honda, Giannopoulos and Milman, and Mikhalkin, the geometry is present in a very vivid and tangible way; combining respectively with topology, analysis and algebra.The papers of Bauer and Seidel, on the other hand, makes the point that algebraic and algebro-topological abstraction (triangulated categories, spectra) can play an important role in very unexpected ways in concrete geometric problems. - From the Preface by the Editors

A Course in Complex Analysis and Riemann Surfaces

Author : Wilhelm Schlag
Publisher : American Mathematical Society
ISBN 13 : 0821898477
Total Pages : 402 pages
Book Rating : 4.8/5 (218 download)

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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.

Complex Geometry

Author : Daniel Huybrechts
Publisher : Springer Science & Business Media
ISBN 13 : 9783540212904
Total Pages : 336 pages
Book Rating : 4.2/5 (129 download)

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Book Synopsis Complex Geometry by : Daniel Huybrechts

Download or read book Complex Geometry written by Daniel Huybrechts and published by Springer Science & Business Media. This book was released on 2005 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

Manifolds of J-holomorphic Discs

Author : Uroš Kuzman
Publisher :
ISBN 13 :
Total Pages : 87 pages
Book Rating : 4.:/5 (852 download)

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Book Synopsis Manifolds of J-holomorphic Discs by : Uroš Kuzman

Download or read book Manifolds of J-holomorphic Discs written by Uroš Kuzman and published by . This book was released on 2013 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the deformation space of $J$-holomorphic discs in an almost complex manifold $(M, J)$. We find a nonlinear invertible operator mapping the space of all small $J$-holomorphic deformations of the given $J$-holomorphic disc on to the space of small holomorphic deformations of the standard disc in $\mathbb{C}^n$. Furthermore, we study the neighborhood of an embedded disc attached along its boundary to a maximal totally real submanifold. In particular, we provide suffcient conditions for the set of all nearby attached $J$-holomorphic discs to be a manifold. Finally, we extend the theorem of E. Poletsky, concerning plurisubharmonicity of the envelope of the Poisson functional of an upper semicontinuous function, to almost complex surfaces of real dimension 4.