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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.
Rational homotopy is a very powerful tool for differential topology
and geometry. This text aims to provide graduates and researchers
with the tools necessary for the use of rational homotopy in
geometry. Algebraic Models in Geometry has been written for
topologists who are drawn to geometrical problems amenable to
topological methods and also for geometers who are faced with
problems requiring topological approaches and thus need a simple
and concrete introduction to rational homotopy. This is essentially
a book of applications. Geodesics, curvature, embeddings of
manifolds, blow-ups, complex and Kahler manifolds, symplectic
geometry, torus actions, configurations and arrangements are all
covered. The chapters related to these subjects act as an
introduction to the topic, a survey, and a guide to the literature.
But no matter what the particular subject is, the central theme of
the book persists; namely, there is a beautiful connection between
geometry and rational homotopy which both serves to solve geometric
problems and spur the development of topological methods.
Rational homotopy is a very powerful tool for differential topology
and geometry. This text aims to provide graduates and researchers
with the tools necessary for the use of rational homotopy in
geometry. Algebraic Models in Geometry has been written for
topologists who are drawn to geometrical problems amenable to
topological methods and also for geometers who are faced with
problems requiring topological approaches and thus need a simple
and concrete introduction to rational homotopy. This is essentially
a book of applications. Geodesics, curvature, embeddings of
manifolds, blow-ups, complex and Kahler manifolds, symplectic
geometry, torus actions, configurations and arrangements are all
covered. The chapters related to these subjects act as an
introduction to the topic, a survey, and a guide to the literature.
But no matter what the particular subject is, the central theme of
the book persists; namely, there is a beautiful connection between
geometry and rational homotopy which both serves to solve geometric
problems and spur the development of topological methods.
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