English

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