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Symplectic Geometry and Secondary Characteristic Classes

  • Izu Vaisman

Part of the Progress in Mathematics book series (PM)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Izu Vaisman
    Pages 1-21
  3. Izu Vaisman
    Pages 23-52
  4. Izu Vaisman
    Pages 53-101
  5. Back Matter
    Pages 207-219

About this book

Introduction

The present work grew out of a study of the Maslov class (e. g. (37]), which is a fundamental invariant in asymptotic analysis of partial differential equations of quantum physics. One of the many in­ terpretations of this class was given by F. Kamber and Ph. Tondeur (43], and it indicates that the Maslov class is a secondary characteristic class of a complex trivial vector bundle endowed with a real reduction of its structure group. (In the basic paper of V. I. Arnold about the Maslov class (2], it is also pointed out without details that the Maslov class is characteristic in the category of vector bundles mentioned pre­ viously. ) Accordingly, we wanted to study the whole range of secondary characteristic classes involved in this interpretation, and we gave a short description of the results in (83]. It turned out that a complete exposition of this theory was rather lengthy, and, moreover, I felt that many potential readers would have to use a lot of scattered references in order to find the necessary information from either symplectic geometry or the theory of the secondary characteristic classes. On the otherhand, both these subjects are of a much larger interest in differential geome­ try and topology, and in the applications to physical theories.

Keywords

Potential cls partial differential equation quantum physics symplectic geometry

Authors and affiliations

  • Izu Vaisman
    • 1
  1. 1.Department of MathematicsUniversity of HaifaMount Carmel, HaifaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-1960-4
  • Copyright Information Birkhäuser Boston 1987
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-1962-8
  • Online ISBN 978-1-4757-1960-4
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site