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Virtual Fundamental Cycles in Symplectic Topology (Hardcover)
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Virtual Fundamental Cycles in Symplectic Topology (Hardcover)
Series: Mathematical Surveys and Monographs
Expected to ship within 12 - 19 working days
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The method of using the moduli space of pseudo-holomorphic curves
on a symplectic manifold was introduced by Mikhail Gromov in 1985.
From the appearance of Gromov's original paper until today this
approach has been the most important tool in global symplectic
geometry. To produce numerical invariants of these manifolds using
this method requires constructing a fundamental cycle associated
with moduli spaces. This volume brings together three approaches to
constructing the ``virtual'' fundamental cycle for the moduli space
of pseudo-holomorphic curves. All approaches are based on the idea
of local Kuranishi charts for the moduli space. Workers in the
field will get a comprehensive understanding of the details of
these constructions and the assumptions under which they can be
made. These techniques and results will be essential in further
applications of this approach to producing invariants of symplectic
manifolds. This book is published in cooperation with Simons Center
for Geometry and Physics.
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