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We show that if a positive integral surgery on a knot K inside a homologysphere X with Seifert genus g(K) results in an induced knot K_n in X_n(K)=Ywhich has simple Floer homology, we should have n>=2g(K). Moreover, if X is thestandard sphere, the three-manifold Y is a L-space and the Heegaard Floerhomology groups of K are determined by its Alexander polynomial.

Knots which admit a surgery with simple knot Floer homology groups