Knots which admit a surgery with simple knot Floer homology groups

Details Knots which admit a surgery with simple knot Floer homology groups Knots which admit a surgery with simple knot Floer homology groups

2010-03-18

arxiv.org/abs/1003.3567v1

Mathematics

Geometric Topology

Scientific paper

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 K_n in X_n(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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