132 research outputs found
Anti-symplectic involution and Floer cohomology
The main purpose of the present paper is a study of orientations of the
moduli spaces of pseudo-holomorphic discs with boundary lying on a \emph{real}
Lagrangian submanifold, i.e., the fixed point set of an anti-symplectic
involutions on a symplectic manifold. We introduce the notion of
-relatively spin structure for an anti-symplectic involution , and
study how the orientations on the moduli space behave under the involution
. We also apply this to the study of Lagrangian Floer theory of real
Lagrangian submanifolds. In particular, we study unobstructedness of the
-fixed point set of symplectic manifolds and in particular prove its
unobstructedness in the case of Calabi-Yau manifolds. And we also do explicit
calculation of Floer cohomology of over
which provides an example whose Floer cohomology is not isomorphic to its
classical cohomology. We study Floer cohomology of the diagonal of the square
of a symplectic manifold, which leads to a rigorous construction of the quantum
Massey product of symplectic manifold in complete generality.Comment: 85 pages, final version, to appear in Geometry and Topolog
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