Framed instanton homology of surgeries on L-space knots

Abstract

An important class of three-manifolds are L-spaces, which are rational homology spheres with the smallest possible Floer homology. For knots with an instanton L-space surgery, we compute the framed instanton Floer homology of all integral surgeries. As a consequence, if a knot has a Heegaard Floer and instanton Floer L-space surgery, then the theories agree for all integral surgeries. In order to prove the main result, we prove that the Baldwin-Sivek contact invariant in framed instanton Floer homology is homogeneous with respect to the absolute $\mathbb{Z}/2$-grading, but not the $\mathbb{Z}/4$-grading.