Mathematics – Algebraic Geometry
Scientific paper
2001-03-12
Adv.Theor.Math.Phys. 5 (2002) 1-49 and Geom. Topol. Monogr. 8 (2006) 1-47
Mathematics
Algebraic Geometry
This is the version published by Geometry & Topology Monographs on 22 April 2006
Scientific paper
10.2140/gtm.2006.8.1
In this paper, we present foundational material towards the development of a rigorous enumerative theory of stable maps with Lagrangian boundary conditions, ie stable maps from bordered Riemann surfaces to a symplectic manifold, such that the boundary maps to a Lagrangian submanifold. Our main application is to a situation where our proposed theory leads to a well-defined algebro-geometric computation very similar to well-known localization techniques in Gromov-Witten theory. In particular, our computation of the invariants for multiple covers of a generic disc bounding a special Lagrangian submanifold in a Calabi-Yau threefold agrees completely with the original predictions of Ooguri and Vafa based on string duality. Our proposed invariants depend more generally on a discrete parameter which came to light in the work of Aganagic, Klemm, and Vafa which was also based on duality, and our more general calculations agree with theirs up to sign.
Katz Sheldon
Liu Chiu-Chu Melissa
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