Transversality for perturbed special Lagrangian submanifolds

Abstract

In this paper, we prove a transversality theorem for the moduli space of perturbed special Lagrangian submanifolds in a 6-dimensional manifold equipped with a generalization of a Calabi-Yau structure. These perturbed special Lagrangian submanifolds arise as solutions to an infinite-dimensional Lagrange multipliers problem which is part of a proposal for counting special Lagrangians outlined by Donaldson and Segal in their paper Gauge theory in higher dimensions II. More specifically, we prove that this moduli space is generically a set of isolated points.

35 pages, 0 figures Changes: Definition of the space of parameters was modified. The results of Theorem 1.2 only apply after this modification. Minor typos also corrected