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＜電子ブック＞
A Course on Holomorphic Discs / by Hansjörg Geiges, Kai Zehmisch
(Birkhäuser Advanced Texts Basler Lehrbücher. ISSN:22964894)

版	1st ed. 2023.
出版者	(Cham : Springer Nature Switzerland : Imprint: Birkhäuser)
出版年	2023
本文言語	英語
大きさ	XVIII, 189 p. 11 illus : online resource
著者標目	*Geiges, Hansjörg author Zehmisch, Kai author SpringerLink (Online service)
件　名	LCSH:Functions of complex variables LCSH:Geometry, Differential LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Functional analysis FREE:Several Complex Variables and Analytic Spaces FREE:Differential Geometry FREE:Global Analysis and Analysis on Manifolds FREE:Functional Analysis
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-031-36064-0

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