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Symplectic Geometry and Secondary Characteristic Classes

  • Book
  • © 1987

Overview

Authors:
  1. Izu Vaisman

    1. Department of Mathematics, University of Haifa, Mount Carmel, Haifa, Israel

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Part of the book series: Progress in Mathematics (PM)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction and Motivation

    • Izu Vaisman
    Pages 1-21

  3. Symplectic Vector Spaces

    • Izu Vaisman
    Pages 23-52

  4. Symplectic Geometry on Manifolds

    • Izu Vaisman
    Pages 53-101

  5. Transversality Obstructions of Lagrangian Subbundles (Maslov Classes)

    • Izu Vaisman
    Pages 103-205

  6. Back Matter

    Pages 207-219
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Haifa, Mount Carmel, Haifa, Israel

    Izu Vaisman

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