03603nam 22006975 450 991073488890332120251113203200.03-031-36064-810.1007/978-3-031-36064-0(CKB)27559760700041(DE-He213)978-3-031-36064-0(MiAaPQ)EBC30766908(Au-PeEL)EBL30766908(PPN)272250813(MiAaPQ)EBC30621363(Au-PeEL)EBL30621363(EXLCZ)992755976070004120230706d2023 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierA Course on Holomorphic Discs /by Hansjörg Geiges, Kai Zehmisch1st ed. 2023.Cham :Springer Nature Switzerland :Imprint: Birkhäuser,2023.1 online resource (XVIII, 189 p. 11 illus.)Birkhäuser Advanced Texts Basler Lehrbücher,2296-48949783031360633 Includes bibliographical references and index.Gromov's Nonsqueezing Theorem -- Compactness -- Bounds of Higher Order -- Elliptic Regularity -- Transversality.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. This 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.Birkhäuser Advanced Texts Basler Lehrbücher,2296-4894Functions of complex variablesGeometry, DifferentialGlobal analysis (Mathematics)Manifolds (Mathematics)Functional analysisSeveral Complex Variables and Analytic SpacesDifferential GeometryGlobal Analysis and Analysis on ManifoldsFunctional AnalysisFunctions of complex variables.Geometry, Differential.Global analysis (Mathematics)Manifolds (Mathematics)Functional analysis.Several Complex Variables and Analytic Spaces.Differential Geometry.Global Analysis and Analysis on Manifolds.Functional Analysis.516.36Geiges Hansjörg429959Zehmisch KaiMiAaPQMiAaPQMiAaPQBOOK9910734888903321A Course on Holomorphic Discs3566871UNINA