Quantum homology of compact convex symplectic manifolds
Symplectic Geometry
2013-02-06 v1
Abstract
We study the space of pseudo-holomorphic spheres in compact symplectic manifolds with convex boundary. We show that the theory of Gromov-Witten invariants can be extended to the class of semi-positive manifolds with convex boundary. This leads to a deformation of intersection products on the absolute and relative singular homologies. As a result, absolute and relative quantum homology algebras are defined analogously to the case of closed symplectic manifolds. In addition, we prove the Poincar\'{e}-Lefschetz duality for the absolute and relative quantum homology algebras.
Keywords
Cite
@article{arxiv.1302.1021,
title = {Quantum homology of compact convex symplectic manifolds},
author = {Sergei Lanzat},
journal= {arXiv preprint arXiv:1302.1021},
year = {2013}
}
Comments
26 pages