A Course on Holomorphic Discs

Hansjörg Geiges, Kai Zehmisch (Autoren)

Buch | Hardcover

XVIII, 189 Seiten

2023 | 2023
Springer International Publishing (Verlag)
978-3-031-36063-3 (ISBN)

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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 independentstudy. 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.

Hansjörg Geiges, born in Basel in 1966, is Professor of Mathematics at the Universität zu Köln. He received his PhD from the University of Cambridge in 1992. Before moving to his current position in 2002, he taught at Stanford University, ETH Zürich, and the Universiteit Leiden. His other published books are An Introduction to Contact Topology and The Geometry of Celestial Mechanics.
Kai Zehmisch, born in Leipzig in 1975, is Professor of Mathematics at the Ruhr-Universitat Bochum. He obtained his doctorate at the Universität Leipzig in 2009, after having lived through the failure of the second socialist experiment on German soil, and was rewarded nonetheless with a book prize on 100 Jahre Mathematisches Seminar der Karl-Marx-Universität Leipzig. Previous to his current position, he taught at the Westfälische Wilhems-Universität Münster (as it was then called) at the Justus-Liebig-Universität Giessen.

Gromov's Nonsqueezing Theorem.- Compactness.- Bounds of Higher Order.- Elliptic Regularity.- Transversality.

Erscheinungsdatum	08.07.2023
Reihe/Serie	Birkhäuser Advanced Texts Basler Lehrbücher
Zusatzinfo	XVIII, 189 p. 11 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	469 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Banach manifolds of maps • Fredholm Theory • moduli spaces • Nonlinear Cauchy-Riemann Operator • Nonsqueezing Theorem • pseudoholomorphic curves • Sard-Smale Theorem • Symplectic Embeddings
ISBN-10	3-031-36063-X / 303136063X
ISBN-13	978-3-031-36063-3 / 9783031360633
Zustand	Neuware