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 with Seifert genus g(K) results in an induced knot Kn in Xn(K)=Y which has simple Floer homology, we should have n>=2g(K). Moreover, if X is the standard sphere, the three-manifold Y is a L-space and the Heegaard Floer homology groups of K are determined by its Alexander polynomial.
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