Sutured instanton homology and Heegaard diagrams

Abstract

Suppose H is an admissible Heegaard diagram for a balanced sutured manifold (M,\gamma). We prove that the number of generators of the associated sutured Heegaard Floer complex is an upper bound on the dimension of the sutured instanton homology of (M,\gamma). It follows, in particular, that strong L-spaces are instanton L-spaces.