Knots which admit a surgery with simple knot Floer homology groups

Abstract

We show that if a positive integral surgery on a knot $K$ inside a homology sphere $X$ results in an induced knot $K_n\subset X_n\left(K\right)=Y$ which has simple Floer homology then $n\ge 2g\left(K\right)$. Moreover, for $X=S^3$ the three-manifold $Y$ is an $L$–space, and the Heegaard Floer homology groups of $K$ are determined by its Alexander polynomial.