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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.
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