On the counting of holomorphic discs in toric Fano manifolds

Abstract

Open Gromov-Witten invariants in general are not well-defined. We discuss in detail the enumerative numbers of the Clifford torus $T^2$ in $\CP^2$. For cyclic A-infinity algebras, we show that certain generalized way of counting may be defined up to Hochschild or cyclic boundary elements. In particular we obtain a well-defined function on Hochschild or cyclic homology of a cyclic A-infinity algebra, which has invariance property under cyclic A-infinity homomorphism. We discuss an example of Clifford torus $T^2$ and compute the invariant for a specific cyclic cohomology class.

17 pages, 2 figures,v2: rewritten using the language of cyclic A-infinity algebra, v3: added an example of a cyclic cohomology class, published version

References in corpus (2)

• Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
• Homological mirror symmetry for the quartic surface

Cited by in corpus (2)

• Kuranishi homology and Kuranishi cohomology
• Strong homotopy inner product of an A-infinity algebra