Exponential Decay Estimates And Smoothness Of The Moduli Space Of Pseudoholomorphic Curves
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Exponential Decay Estimates And Smoothness Of The Moduli Space Of Pseudoholomorphic Curves
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Author : Kenji Fukaya
language : en
Publisher: American Mathematical Society
Release Date : 2024-08-19
Exponential Decay Estimates And Smoothness Of The Moduli Space Of Pseudoholomorphic Curves written by Kenji Fukaya 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 2024-08-19 with Mathematics categories.
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Polyfold And Fredholm Theory
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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.
Kuranishi Structures And Virtual Fundamental Chains
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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.
Wellposedness Of Second Order Master Equations For Mean Field Games With Nonsmooth Data
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Author : Chenchen Mou
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-13
Wellposedness Of Second Order Master Equations For Mean Field Games With Nonsmooth Data written by Chenchen Mou 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 2024-12-13 with Mathematics categories.
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On The Nodal Set Of Solutions To A Class Of Nonlocal Parabolic Equations
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Author : Alessandro Audrito
language : en
Publisher: American Mathematical Society
Release Date : 2024-10-23
On The Nodal Set Of Solutions To A Class Of Nonlocal Parabolic Equations written by Alessandro Audrito 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 2024-10-23 with Mathematics categories.
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Amenability And Weak Containment For Actions Of Locally Compact Groups On C Algebras
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Author : Alcides Buss
language : en
Publisher: American Mathematical Society
Release Date : 2024-10-23
Amenability And Weak Containment For Actions Of Locally Compact Groups On C Algebras written by Alcides Buss 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 2024-10-23 with Mathematics categories.
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On Hydrodynamic Limits Of The Vlasov Navier Stokes System
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Author : Daniel Han-Kwan
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-13
On Hydrodynamic Limits Of The Vlasov Navier Stokes System written by Daniel Han-Kwan 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 2024-12-13 with Mathematics categories.
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The Strong K Nneth Theorem For Topological Periodic Cyclic Homology
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Author : Andrew J. Blumberg
language : en
Publisher: American Mathematical Society
Release Date : 2024-10-23
The Strong K Nneth Theorem For Topological Periodic Cyclic Homology written by Andrew J. Blumberg 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 2024-10-23 with Mathematics categories.
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The Motivic Anabelian Geometry Of Local Heights On Abelian Varieties
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Author : L. Alexander Betts
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-13
The Motivic Anabelian Geometry Of Local Heights On Abelian Varieties written by L. Alexander Betts 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 2024-12-13 with Mathematics categories.
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Symbolic Dynamics For Nonuniformly Hyperbolic Maps With Singularities In High Dimension
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Author : Ermerson Araujo
language : en
Publisher: American Mathematical Society
Release Date : 2024-10-23
Symbolic Dynamics For Nonuniformly Hyperbolic Maps With Singularities In High Dimension written by Ermerson Araujo 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 2024-10-23 with Mathematics categories.
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