Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory write by Chris Wendl. This book was released on 2020-03-26. Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory available in PDF, EPUB and Kindle. An accessible introduction to the intersection theory of punctured holomorphic curves and its applications in topology.
Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory
Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory write by Chris Wendl. This book was released on 2020-03-26. Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory available 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.
Holomorphic Curves in Low Dimensions
Holomorphic Curves in Low Dimensions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Holomorphic Curves in Low Dimensions write by Chris Wendl. This book was released on 2018-06-28. Holomorphic Curves in Low Dimensions available 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
Advances in Mathematical Sciences
Advances in Mathematical Sciences - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in Mathematical Sciences write by Bahar Acu. This book was released on 2020-07-16. Advances in Mathematical Sciences available 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
A Course on Holomorphic Discs
A Course on Holomorphic Discs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Course on Holomorphic Discs write by Hansjörg Geiges. This book was released on 2023-08-07. A Course on Holomorphic Discs available 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.
