enumerative invariants for stable

A-branes, foliations and localization

We study a notion of enumerative invariants for stable and discuss its relation to invariants defined by spectral and exponential networks.A natural definition of stable and their counts is provided by the string theoretic origin of the topological.This is the witten index of the supersymmetric quantum mechanics of a single branesupported on a special lagrangian in a calabi-yau threefold.Geometrically, this is closely related to the euler characteristic of the moduli space.Using the natural torus action on this moduli space, we reduce the computation of its euler characteristic to a count of fixed points via equivariant localization.We find agreement between the counts defined via the witten index, and the bpsinvariants defined by networks.