A Course on Holomorphic Discs

 
A Course on Holomorphic Discs
Free Download A Course on Holomorphic Discs
English | 2023 | ISBN: 303136063X | 203 Pages | PDF (True) | 4.3 MB
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.


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Holomorphic Curves in Symplectic Geometry

 
Holomorphic Curves in Symplectic Geometry
Free Download Holomorphic Curves in Symplectic Geometry by Michèle Audin, Jacques Lafontaine
English | PDF | 1994 | 333 Pages | ISBN : 3764329971 | 44.2 MB
This book is devoted to pseudo-holomorphic curve methods in symplectic geometry. It contains an introduction to symplectic geometry and relevant techniques of Riemannian geometry, proofs of Gromov's compactness theorem, an investigation of local properties of holomorphic curves, including positivity of intersections, and applications to Lagrangian embeddings problems. The chapters are based on a series of lectures given previously by the authors M. Audin, A. Banyaga, P. Gauduchon, F. Labourie, J. Lafontaine, F. Lalonde, Gang Liu, D. McDuff, M.-P. Muller, P. Pansu, L. Polterovich, J.C. Sikorav. In an attempt to make this book accessible also to graduate students, the authors provide the necessary examples and techniques needed to understand the applications of the theory. The exposition is essentially self-contained and includes numerous exercises.


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Holomorphic Dynamics on Hyperbolic Riemann Surfaces

 
Holomorphic Dynamics on Hyperbolic Riemann Surfaces
Abate, "Holomorphic Dynamics on Hyperbolic Riemann Surfaces "
English | ISBN: 3110601052 | 2022 | 400 pages | PDF | 7 MB
This completely revised and updated edition of the one variable part of the author's classic older book "Iteration Theory of Holomorphic Maps on Taut Manifolds" presents the theory of holomorphic dynamical systems on hyperbolic Riemann surfaces from the very beginning of the subject up to the most recent developments. It is intended both as a reference book for the experts and as an accessible gateway to this beautiful theory for Master and Ph.D. students. It also contains extensive historical notes and references for further readings.


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