Symplectic Manifolds with no Kähler Structure / by Aleksy Tralle, John Oprea.

Format:

Book

Author/Creator:

Tralle, Aleksy, 1958- author.

Oprea, John, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1661.

Lecture Notes in Mathematics, 0075-8434 ; 1661

Language:

English

Subjects (All):

Global differential geometry.

Algebraic topology.

Differential Geometry.

Algebraic Topology.

Local Subjects:

Differential Geometry.

Algebraic Topology.

Physical Description:

1 online resource (VIII, 208 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997.

System Details:

text file PDF

Summary:

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.

Contents:

The starting point: Homotopy properties of kähler manifolds

Nilmanifolds

Solvmanifolds

The examples of McDuff

Symplectic structures in total spaces of bundles

Survey.

Other Format:

Printed edition:

ISBN:

9783540691457

Access Restriction:

Restricted for use by site license.