Sutured instanton homology and Heegaard diagrams

TL;DR

This paper establishes an upper bound on the dimension of sutured instanton homology using generators from sutured Heegaard Floer complexes, linking properties of L-spaces in different homology theories.

Contribution

It proves that the number of generators from an admissible Heegaard diagram bounds the sutured instanton homology dimension, connecting sutured Floer and instanton theories.

Findings

Number of generators bounds sutured instanton homology dimension

Strong L-spaces are also instanton L-spaces

Provides new inequalities relating Heegaard Floer and instanton invariants

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.