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

Eftekhary, Eaman

Algebr. Geom. Topol. 11, No. 3, 1243-1256 (2011).

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.

MSC:

57M27	Invariants of knots and \(3\)-manifolds (MSC2010)
57R58	Floer homology

Keywords:

simple knot Floer homology; \(L\)-space surgery

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