Quantum homology of compact convex symplectic manifolds

2013/02/05 by Sergei Lanzat, Lanzat, Sergei
Mathematics · #53D05 #53D45 #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG #msc:53D05 #msc:53D45

paper · pdf · doi:10.48550/arxiv.1302.1021

26 pages

arxiv created 2013/02/05 · arxiv updated 2013/02/06

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 Poincaré-Lefschetz duality for the absolute and relative quantum homology algebras.

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