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Symplectic geometry and topology is a tremendously explosive area
with strong connections linking differential geometry to algebraic
topology. Since Kahler manifolds were the first compact examples of
symplectic manifolds, the first question that arises is whether all
compact symplectic manifolds are Kahler. As is typical in the subject,
either the simply connected or non-simply connected case is easy while
the other is hard. In this case, non-simply connected non-Kahler
symplectic manifolds are easy to find. The simply connected situation
is harder. This book gives an exposition of these types of examples
as well as a general approach to such questions via rational homotopy theory.
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