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  • © 1997

Symplectic Manifolds with no Kaehler structure

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

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-viii
  2. Nilmanifolds

    • Aleksy Tralle, John Oprea
    Pages 45-69
  3. Solvmanifolds

    • Aleksy Tralle, John Oprea
    Pages 70-119
  4. The examples of McDuff

    • Aleksy Tralle, John Oprea
    Pages 120-136
  5. Symplectic structures in total spaces of bundles

    • Aleksy Tralle, John Oprea
    Pages 137-172
  6. Survey

    • Aleksy Tralle, John Oprea
    Pages 173-199
  7. Back Matter

    Pages 200-207

About this book

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

  • Book Title: Symplectic Manifolds with no Kaehler structure

  • Authors: Aleksy Tralle, John Oprea

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0092608

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Softcover ISBN: 978-3-540-63105-7Published: 17 July 1997

  • eBook ISBN: 978-3-540-69145-7Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 208

  • Topics: Differential Geometry, Algebraic Topology

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions