The geometry of infinite-dimensional groups
By: Boris Khesin, Robert Wendt
Contributors: Wendt, Robert; SpringerLink (Online service)
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete = -- Series of modern surveys in mathematics -- 3. Folge, v. 51
Publisher: Springer
Published: 2009
Place of publication: Berlin; London
Language: eng
Number of pages: 304
ISBN-13: 9783540772637; 9783540772620; 9783540852056
Subjects: Infinite dimensional Lie algebras; Lie groups
Description: 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.
Notes: Includes bibliographical references (p. [281]-300) and index.