Knots which admit a surgery with simple knot Floer homology groups. (English) Zbl 1258.57006

Summary: We show that if a positive integral surgery on a knot \(K\) inside a homology sphere \(X\) results in an induced knot \(K_n \subset X_n(K) = Y\) which has simple Floer homology, then \(n \geq 2g(K)\). 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.


57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57R58 Floer homology
Full Text: DOI arXiv


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