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Symplectic Manifolds with no Kähler Structure

  • Authors
  • Aleksy Tralle
  • John Oprea

Part of the Lecture Notes in Mathematics book series (LNM, volume 1661)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Aleksy Tralle, John Oprea
    Pages 45-69
  3. Aleksy Tralle, John Oprea
    Pages 70-119
  4. Aleksy Tralle, John Oprea
    Pages 120-136
  5. Aleksy Tralle, John Oprea
    Pages 137-172
  6. Aleksy Tralle, John Oprea
    Pages 173-199
  7. Back Matter
    Pages 200-207

About this book

Introduction

This is a research monograph covering the majority of known results on the problem of constructing compact symplectic manifolds with no Kaehler structure with an emphasis on the use of rational homotopy theory. In recent years, some new and stimulating conjectures and problems have been formulated due to an influx of homotopical ideas. Examples include the Lupton-Oprea conjecture, the Benson-Gordon conjecture, both of which are in the spirit of some older and still unsolved problems (e.g. Thurston's conjecture and Sullivan's problem). Our explicit aim is to clarify the interrelations between certain aspects of symplectic geometry and homotopy theory in the framework of the problems mentioned above. We expect that the reader is aware of the basics of differential geometry and algebraic topology at graduate level.

Keywords

Algebraic topology Arnold's conjecture Homotopy Weinstein's problem differential geometry homotopy theory manifold rational homotopy theory symplectic geometry

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0092608
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-63105-7
  • Online ISBN 978-3-540-69145-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site