#### Volume 11, issue 3 (2011)

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Knots which admit a surgery with simple knot Floer homology groups

### Eaman Eftekhary

Algebraic & Geometric Topology 11 (2011) 1243–1256
##### 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.

##### Keywords
simple knot Floer homology, L–space surgery
Primary: 57M27
Secondary: 57R58