Applications Of Polyfold Theory I The Polyfolds Of Gromov Witten Theory

DOWNLOAD

Download Applications Of Polyfold Theory I The Polyfolds Of Gromov Witten Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Applications Of Polyfold Theory I The Polyfolds Of Gromov Witten Theory book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Applications Of Polyfold Theory I The Polyfolds Of Gromov Witten Theory

DOWNLOAD
Author : H. Hofer
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-07-13

Applications Of Polyfold Theory I The Polyfolds Of Gromov Witten Theory written by H. Hofer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-13 with Mathematics categories.

In this paper the authors start with the construction of the symplectic field theory (SFT). As a general theory of symplectic invariants, SFT has been outlined in Introduction to symplectic field theory (2000), by Y. Eliashberg, A. Givental and H. Hofer who have predicted its formal properties. The actual construction of SFT is a hard analytical problem which will be overcome be means of the polyfold theory due to the present authors. The current paper addresses a significant amount of the arising issues and the general theory will be completed in part II of this paper. To illustrate the polyfold theory the authors use the results of the present paper to describe an alternative construction of the Gromov-Witten invariants for general compact symplectic manifolds.

Applications Of Polyfold Theory I

DOWNLOAD
Author : Helmut Hofer
language : en
Publisher:
Release Date : 2017

Applications Of Polyfold Theory I written by Helmut Hofer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Gromov-Witten invariants categories.

In this paper the authors start with the construction of the symplectic field theory (SFT). As a general theory of symplectic invariants, SFT has been outlined in Introduction to symplectic field theory (2000), by Y. Eliashberg, A. Givental and H. Hofer who have predicted its formal properties. The actual construction of SFT is a hard analytical problem which will be overcome be means of the polyfold theory due to the present authors. The current paper addresses a significant amount of the arising issues and the general theory will be completed in part II of this paper. To illustrate the polyf.

Polyfold And Fredholm Theory

DOWNLOAD
Author : Helmut Hofer
language : en
Publisher: Springer Nature
Release Date : 2021-07-21

Polyfold And Fredholm Theory written by Helmut Hofer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-21 with Mathematics categories.

This book pioneers a nonlinear Fredholm theory in a general class of spaces called polyfolds. The theory generalizes certain aspects of nonlinear analysis and differential geometry, and combines them with a pinch of category theory to incorporate local symmetries. On the differential geometrical side, the book introduces a large class of `smooth’ spaces and bundles which can have locally varying dimensions (finite or infinite-dimensional). These bundles come with an important class of sections, which display properties reminiscent of classical nonlinear Fredholm theory and allow for implicit function theorems. Within this nonlinear analysis framework, a versatile transversality and perturbation theory is developed to also cover equivariant settings. The theory presented in this book was initiated by the authors between 2007-2010, motivated by nonlinear moduli problems in symplectic geometry. Such problems are usually described locally as nonlinear elliptic systems, and they have to be studied up to a notion of isomorphism. This introduces symmetries, since such a system can be isomorphic to itself in different ways. Bubbling-off phenomena are common and have to be completely understood to produce algebraic invariants. This requires a transversality theory for bubbling-off phenomena in the presence of symmetries. Very often, even in concrete applications, geometric perturbations are not general enough to achieve transversality, and abstract perturbations have to be considered. The theory is already being successfully applied to its intended applications in symplectic geometry, and should find applications to many other areas where partial differential equations, geometry and functional analysis meet. Written by its originators, Polyfold and Fredholm Theory is an authoritative and comprehensive treatise of polyfold theory. It will prove invaluable for researchers studying nonlinear elliptic problems arising in geometric contexts.

Lectures On Geometry

DOWNLOAD
Author : Nicholas Michael John Woodhouse
language : en
Publisher: Oxford University Press
Release Date : 2017

Lectures On Geometry written by Nicholas Michael John Woodhouse and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.

This book contains a series of chapters by leading researchers and practitioners on community engagement approaches in the field of counterterrorism and counterinsurgency. It presents existing and emerging community engagement models in various parts of the world which could serve as effective models for governments keen to work with community leaders to manage and reduce the terrorist threat. The book emphasizes the strength of communities as central to government approaches in countering violent extremism.

Virtual Fundamental Cycles In Symplectic Topology

DOWNLOAD
Author : John W. Morgan
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-04-12

Virtual Fundamental Cycles In Symplectic Topology written by John W. Morgan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-12 with Mathematics categories.

The method of using the moduli space of pseudo-holomorphic curves on a symplectic manifold was introduced by Mikhail Gromov in 1985. From the appearance of Gromov's original paper until today this approach has been the most important tool in global symplectic geometry. To produce numerical invariants of these manifolds using this method requires constructing a fundamental cycle associated with moduli spaces. This volume brings together three approaches to constructing the “virtual” fundamental cycle for the moduli space of pseudo-holomorphic curves. All approaches are based on the idea of local Kuranishi charts for the moduli space. Workers in the field will get a comprehensive understanding of the details of these constructions and the assumptions under which they can be made. These techniques and results will be essential in further applications of this approach to producing invariants of symplectic manifolds.

Orientability Of Moduli Spaces And Open Gromov Witten Invariants

DOWNLOAD
Author : Penka Vasileva Georgieva
language : en
Publisher: Stanford University
Release Date : 2011

Orientability Of Moduli Spaces And Open Gromov Witten Invariants written by Penka Vasileva Georgieva and has been published by Stanford University this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.

We show that the local system of orientations on the moduli space of J-holomorphic maps from a bordered Riemann surface is isomorphic to the pull-back of a local system defined on the product of the Lagrangian and its free loop space. The latter is defined using only the first and second Stiefel-Whitney classes of the Lagrangian. In the presence of an anti-symplectic involution, whose fixed locus is a relatively spin Lagrangian, we define open Gromov-Witten type invariants in genus zero.

J Holomorphic Curves And Symplectic Topology

DOWNLOAD
Author : Dusa McDuff
language : en
Publisher: American Mathematical Society
Release Date : 2025-01-03

J Holomorphic Curves And Symplectic Topology written by Dusa McDuff and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-03 with Mathematics categories.

The theory of $J$-holomorphic curves has been of great importance since its introduction by Gromov in 1985. In mathematics, its applications include many key results in symplectic topology. It was also one of the main inspirations for the creation of Floer homology. In mathematical physics, it provides a natural context in which to define Gromov–Witten invariants and quantum cohomology, two important ingredients of the mirror symmetry conjecture. The main goal of this book is to establish the fundamental theorems of the subject in full and rigorous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associativity of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology: there are two long chapters on applications, one concentrating on classical results in symplectic topology and the other concerned with quantum cohomology. The last chapter sketches some recent developments in Floer theory. The five appendices of the book provide necessary background related to the classical theory of linear elliptic operators, Fredholm theory, Sobolev spaces, as well as a discussion of the moduli space of genus zero stable curves and a proof of the positivity of intersections of $J$-holomorphic curves in four-dimensional manifolds. The second edition clarifies various arguments, corrects several mistakes in the first edition, includes some additional results in Chapter 10 and Appendices C and D, and updates the references to recent developments.

Kuranishi Structures And Virtual Fundamental Chains

DOWNLOAD
Author : Kenji Fukaya
language : en
Publisher: Springer Nature
Release Date : 2020-10-16

Kuranishi Structures And Virtual Fundamental Chains written by Kenji Fukaya and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-16 with Mathematics categories.

The package of Gromov’s pseudo-holomorphic curves is a major tool in global symplectic geometry and its applications, including mirror symmetry and Hamiltonian dynamics. The Kuranishi structure was introduced by two of the authors of the present volume in the mid-1990s to apply this machinery on general symplectic manifolds without assuming any specific restrictions. It was further amplified by this book’s authors in their monograph Lagrangian Intersection Floer Theory and in many other publications of theirs and others. Answering popular demand, the authors now present the current book, in which they provide a detailed, self-contained explanation of the theory of Kuranishi structures. Part I discusses the theory on a single space equipped with Kuranishi structure, called a K-space, and its relevant basic package. First, the definition of a K-space and maps to the standard manifold are provided. Definitions are given for fiber products, differential forms, partitions of unity, and the notion of CF-perturbations on the K-space. Then, using CF-perturbations, the authors define the integration on K-space and the push-forward of differential forms, and generalize Stokes' formula and Fubini's theorem in this framework. Also, “virtual fundamental class” is defined, and its cobordism invariance is proved. Part II discusses the (compatible) system of K-spaces and the process of going from “geometry” to “homological algebra”. Thorough explanations of the extension of given perturbations on the boundary to the interior are presented. Also explained is the process of taking the “homotopy limit” needed to handle a system of infinitely many moduli spaces. Having in mind the future application of these chain level constructions beyond those already known, an axiomatic approach is taken by listing the properties of the system of the relevant moduli spaces and then a self-contained account of the construction of the associated algebraic structures is given. This axiomatic approach makes the exposition contained here independent of previously published construction of relevant structures.

Research Directions In Symplectic And Contact Geometry And Topology

DOWNLOAD
Author : Bahar Acu
language : en
Publisher: Springer Nature
Release Date : 2022-02-02

Research Directions In Symplectic And Contact Geometry And Topology written by Bahar Acu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-02 with Mathematics categories.

This book highlights a number of recent research advances in the field of symplectic and contact geometry and topology, and related areas in low-dimensional topology. This field has experienced significant and exciting growth in the past few decades, and this volume provides an accessible introduction into many active research problems in this area. The papers were written with a broad audience in mind so as to reach a wide range of mathematicians at various levels. Aside from teaching readers about developing research areas, this book will inspire researchers to ask further questions to continue to advance the field. The volume contains both original results and survey articles, presenting the results of collaborative research on a wide range of topics. These projects began at the Research Collaboration Conference for Women in Symplectic and Contact Geometry and Topology (WiSCon) in July 2019 at ICERM, Brown University. Each group of authors included female and nonbinary mathematicians at different career levels in mathematics and with varying areas of expertise. This paved the way for new connections between mathematicians at all career levels, spanning multiple continents, and resulted in the new collaborations and directions that are featured in this work.

Holomorphic Curves In Low Dimensions

DOWNLOAD
Author : Chris Wendl
language : en
Publisher: Springer
Release Date : 2018-06-28

Holomorphic Curves In Low Dimensions written by Chris Wendl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-28 with Mathematics categories.

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