The Geometry of Infinite-Dimensional Groups

  • Boris Khesin
  • Robert Wendt
Book
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (volume 51)

Table of contents

About this book

Introduction

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.

Keywords

Euler equations Gauge theory Hamiltonian systems differential geometry infinite-dimensional Lie groups integrable systems moduli space

Authors and affiliations

  • Boris Khesin
    • 1
  • Robert Wendt
    • 1
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-77263-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-77262-0
  • Online ISBN 978-3-540-77263-7
  • About this book