Kai Zehmisch: A Course on Holomorphic Discs

Cover: 9783031360633 | A Course on Holomorphic Discs | Kai Zehmisch (u. a.) | Buch | xviii

Rückseite: 9783031360633 | A Course on Holomorphic Discs | Kai Zehmisch (u. a.) | Buch | xviii

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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) and at the Justus-Liebig-Universität Giessen.

Zusammenfassung

Provides a self-contained, comprehensive introduction to the theory of pseudoholomorphic curves

Utilizes the proof of a basic theorem to motivate study of advanced topics in symplectic geometry

Suitable for use in a graduate course or for independent study

Inhaltsverzeichnis

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

Details

Erscheinungsjahr:	2023
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xviii 189 S. 11 s/w Illustr. 189 p. 11 illus.
ISBN-13:	9783031360633
ISBN-10:	303136063X
Sprache:	Englisch
Einband:	Gebunden
Autor:	Zehmisch, Kai Geiges, Hansjörg
Hersteller:	Springer Nature Switzerland Springer International Publishing Springer International Publishing AG
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	241 x 160 x 17 mm
Von/Mit:	Kai Zehmisch (u. a.)
Erscheinungsdatum:	07.07.2023
Gewicht:	0,483 kg

Artikel-ID: 126937325