Transversality for perturbed special Lagrangian submanifolds

TL;DR

This paper establishes a transversality result for the moduli space of perturbed special Lagrangian submanifolds in a 6-dimensional manifold, ensuring generic conditions lead to isolated solutions, advancing understanding in higher-dimensional gauge theory.

Contribution

It proves a transversality theorem for the moduli space of perturbed special Lagrangian submanifolds, demonstrating that generically this space consists of isolated points, which is new in the context of generalized Calabi-Yau structures.

Findings

Moduli space is generically a set of isolated points.

Transversality holds for perturbed special Lagrangians in 6D.

Supports gauge theory approaches in higher dimensions.

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.