Lectures On Contact 3 Manifolds Holomorphic Curves And Intersection Theory PDF Download
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Author | : Chris Wendl |
Publisher | : Cambridge University Press |
Total Pages | : 197 |
Release | : 2020-03-26 |
Genre | : Mathematics |
ISBN | : 1108497403 |
Download Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory Book in PDF, ePub and Kindle
An accessible introduction to the intersection theory of punctured holomorphic curves and its applications in topology.
Author | : Chris Wendl |
Publisher | : Cambridge University Press |
Total Pages | : 198 |
Release | : 2020-03-26 |
Genre | : Mathematics |
ISBN | : 1108759580 |
Download Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory Book in PDF, ePub and Kindle
Intersection theory has played a prominent role in the study of closed symplectic 4-manifolds since Gromov's famous 1985 paper on pseudoholomorphic curves, leading to myriad beautiful rigidity results that are either inaccessible or not true in higher dimensions. Siefring's recent extension of the theory to punctured holomorphic curves allowed similarly important results for contact 3-manifolds and their symplectic fillings. Based on a series of lectures for graduate students in topology, this book begins with an overview of the closed case, and then proceeds to explain the essentials of Siefring's intersection theory and how to use it, and gives some sample applications in low-dimensional symplectic and contact topology. The appendices provide valuable information for researchers, including a concise reference guide on Siefring's theory and a self-contained proof of a weak version of the Micallef–White theorem.
Author | : Chris Wendl |
Publisher | : Springer |
Total Pages | : 294 |
Release | : 2018-06-28 |
Genre | : Mathematics |
ISBN | : 3319913719 |
Download Holomorphic Curves in Low Dimensions Book in PDF, ePub and Kindle
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
Author | : Bahar Acu |
Publisher | : Springer Nature |
Total Pages | : 364 |
Release | : 2020-07-16 |
Genre | : Mathematics |
ISBN | : 3030426874 |
Download Advances in Mathematical Sciences Book in PDF, ePub and Kindle
This volume highlights the mathematical research presented at the 2019 Association for Women in Mathematics (AWM) Research Symposium held at Rice University, April 6-7, 2019. The symposium showcased research from women across the mathematical sciences working in academia, government, and industry, as well as featured women across the career spectrum: undergraduates, graduate students, postdocs, and professionals. The book is divided into eight parts, opening with a plenary talk and followed by a combination of research paper contributions and survey papers in the different areas of mathematics represented at the symposium: algebraic combinatorics and graph theory algebraic biology commutative algebra analysis, probability, and PDEs topology applied mathematics mathematics education
Author | : Hansjörg Geiges |
Publisher | : Springer Nature |
Total Pages | : 203 |
Release | : 2023-08-07 |
Genre | : Mathematics |
ISBN | : 3031360648 |
Download A Course on Holomorphic Discs Book in PDF, ePub and Kindle
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.
Author | : Hideaki Ikoma |
Publisher | : Cambridge University Press |
Total Pages | : 180 |
Release | : 2022-02-03 |
Genre | : Mathematics |
ISBN | : 1108998194 |
Download The Mordell Conjecture Book in PDF, ePub and Kindle
The Mordell conjecture (Faltings's theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least two has only finitely many rational points. This book provides a self-contained and detailed proof of the Mordell conjecture following the papers of Bombieri and Vojta. Also acting as a concise introduction to Diophantine geometry, the text starts from basics of algebraic number theory, touches on several important theorems and techniques (including the theory of heights, the Mordell–Weil theorem, Siegel's lemma and Roth's lemma) from Diophantine geometry, and culminates in the proof of the Mordell conjecture. Based on the authors' own teaching experience, it will be of great value to advanced undergraduate and graduate students in algebraic geometry and number theory, as well as researchers interested in Diophantine geometry as a whole.
Author | : Charles R. Johnson |
Publisher | : Cambridge University Press |
Total Pages | : 223 |
Release | : 2020-10-01 |
Genre | : Mathematics |
ISBN | : 1108800378 |
Download Matrix Positivity Book in PDF, ePub and Kindle
Matrix positivity is a central topic in matrix theory: properties that generalize the notion of positivity to matrices arose from a large variety of applications, and many have also taken on notable theoretical significance, either because they are natural or unifying. This is the first book to provide a comprehensive and up-to-date reference of important material on matrix positivity classes, their properties, and their relations. The matrix classes emphasized in this book include the classes of semipositive matrices, P-matrices, inverse M-matrices, and copositive matrices. This self-contained reference will be useful to a large variety of mathematicians, engineers, and social scientists, as well as graduate students. The generalizations of positivity and the connections observed provide a unique perspective, along with theoretical insight into applications and future challenges. Direct applications can be found in data analysis, differential equations, mathematical programming, computational complexity, models of the economy, population biology, dynamical systems and control theory.
Author | : Christian Rosendal |
Publisher | : Cambridge University Press |
Total Pages | : 309 |
Release | : 2021-12-16 |
Genre | : Mathematics |
ISBN | : 1108905196 |
Download Coarse Geometry of Topological Groups Book in PDF, ePub and Kindle
This book provides a general framework for doing geometric group theory for many non-locally-compact topological transformation groups that arise in mathematical practice, including homeomorphism and diffeomorphism groups of manifolds, isometry groups of separable metric spaces and automorphism groups of countable structures. Using Roe's framework of coarse structures and spaces, the author defines a natural coarse geometric structure on all topological groups. This structure is accessible to investigation, especially in the case of Polish groups, and often has an explicit description, generalising well-known structures in familiar cases including finitely generated discrete groups, compactly generated locally compact groups and Banach spaces. In most cases, the coarse geometric structure is metrisable and may even be refined to a canonical quasimetric structure on the group. The book contains many worked examples and sufficient introductory material to be accessible to beginning graduate students. An appendix outlines several open problems in this young and rich theory.
Author | : János Kollár |
Publisher | : Cambridge University Press |
Total Pages | : 491 |
Release | : 2023-04-30 |
Genre | : Mathematics |
ISBN | : 1009346105 |
Download Families of Varieties of General Type Book in PDF, ePub and Kindle
The first complete treatment of the moduli theory of varieties of general type, laying foundations for future research.
Author | : Alexander Komech |
Publisher | : Cambridge University Press |
Total Pages | : |
Release | : 2021-09-30 |
Genre | : Mathematics |
ISBN | : 100903605X |
Download Attractors of Hamiltonian Nonlinear Partial Differential Equations Book in PDF, ePub and Kindle
This monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits. The text includes many physically relevant examples and will be of interest to graduate students and researchers in both mathematics and physics. The proofs involve novel applications of methods of harmonic analysis, including Tauberian theorems, Titchmarsh's convolution theorem, and the theory of quasimeasures. As well as the underlying theory, the authors discuss the results of numerical simulations and formulate open problems to prompt further research.