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024 7 $a10.1007/978-3-031-36064-0
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035   $a(DE-He213)978-3-031-36064-0
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100   $a20230706d2023      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 12$aA Course on Holomorphic Discs /$fby Hansjörg Geiges, Kai Zehmisch
205   $a1st ed. 2023.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2023.
215   $a1 online resource (XVIII, 189 p. 11 illus.)
225 1 $aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894
311 08$a9783031360633 
320   $aIncludes bibliographical references and index.
327   $aGromov's Nonsqueezing Theorem -- Compactness -- Bounds of Higher Order -- Elliptic Regularity -- Transversality.
330   $aThis textbook, based on a one-semester course taught several times by the authors, provides a self-contained, comprehensive yet concise introduction to the theory of pseudoholomorphic curves. Gromov?s nonsqueezing theorem in symplectic topology is taken as a motivating example, and a complete proof using pseudoholomorphic discs is presented. A sketch of the proof is discussed in the first chapter, with succeeding chapters guiding the reader through the details of the mathematical methods required to establish compactness, regularity, and transversality results. Concrete examples illustrate many of the more complicated concepts, and well over 100 exercises are distributed throughout the text. This approach helps the reader to gain a thorough understanding of the powerful analytical tools needed for the study of more advanced topics in symplectic topology. This text can be used as the basis for a graduate course, and it is also immensely suitable for independent study. Prerequisites include complex analysis, differential topology, and basic linear functional analysis; no prior knowledge of symplectic geometry is assumed. This book is also part of the Virtual Series on Symplectic Geometry.
410  0$aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894
606   $aFunctions of complex variables
606   $aGeometry, Differential
606   $aGlobal analysis (Mathematics)
606   $aManifolds (Mathematics)
606   $aFunctional analysis
606   $aSeveral Complex Variables and Analytic Spaces
606   $aDifferential Geometry
606   $aGlobal Analysis and Analysis on Manifolds
606   $aFunctional Analysis
615  0$aFunctions of complex variables.
615  0$aGeometry, Differential.
615  0$aGlobal analysis (Mathematics)
615  0$aManifolds (Mathematics)
615  0$aFunctional analysis.
615 14$aSeveral Complex Variables and Analytic Spaces.
615 24$aDifferential Geometry.
615 24$aGlobal Analysis and Analysis on Manifolds.
615 24$aFunctional Analysis.
676   $a516.36
700   $aGeiges$b Hansjo?rg$0429959
702   $aZehmisch$b Kai
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910734888903321
996   $aA Course on Holomorphic Discs$93566871
997   $aUNINA