The Geometry of Infinite-Dimensional Groups

• Κύριοι συγγραφείς: Khesin, Boris (Συγγραφέας), Wendt, Robert (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Σειρά: Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics ; 51
• Θέματα: Mathematics.; Algebraic geometry.; Group theory.; Topological groups.; Lie groups.; Global analysis (Mathematics).; Manifolds (Mathematics).; Geometry.; Physics.; Topological Groups, Lie Groups.; Group Theory and Generalizations.; Mathematical Methods in Physics.; Global Analysis and Analysis on Manifolds.; Algebraic Geometry.
• Φυσική περιγραφή: XII, 304 p. online resource.
• ISBN: 9783540772637

This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. While infinite-dimensional groups often exhibit very peculiar features, this book describes unifying geometric ideas of the theory and gives numerous illustrations and examples, ranging from the classification of the Virasoro coadjoint orbits to knot theory, from optimal mass transport to moduli spaces of flat connections on surfaces. The text includes many exercises and open questions, and it is accessible to both students and researchers in Lie theory, geometry, and Hamiltonian systems.