Fibered simple knots

  title={Fibered simple knots},
  author={Joshua Evan Greene and John S Luecke},
  journal={Advances in Mathematics},
1 Citations

On Floer minimal knots in sutured manifolds

It is known that the rank of the sutured Floer homology of <inline-formula content-type="math/mathml"> is a rationally null-homologous knot in <mml:math xmlns:mml="" alttext="upper M">.



Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology

Similar to knots in S 3 , any knot in a lens space has a grid diagram from which one can combinatorially compute all of its knot Floer homology invariants. We give an explicit description of the

L-space surgeries, genus bounds, and the cabling conjecture

We prove that if positive integer p-surgery along a knot K \subset S^3 produces an L-space and it bounds a sharp 4-manifold, then the knot genus obeys the bound 2g(K) -1 \leq p - \sqrt{3p+1}.

On Floer homology and the Berge conjecture on knots admitting lens space surgeries

We complete the first step in a two-part program proposed by Baker, Grigsby, and the author to prove that Berge’s construction of knots in the three-sphere which admit lens space surgeries is

On knot Floer homology and lens space surgeries

The lens space realization problem

We determine the lens spaces that arise by integer Dehn surgery along a knot in the three-sphere. Specically, if surgery along a knot produces a lens space, then there exists an equivalent surgery

A spanning tree model for the Heegaard Floer homology of a branched double‐cover

Given a diagram of a link K in S3, we write down a Heegaard diagram for the branched‐double cover Σ(K). The generators of the associated Heegaard Floer chain complex correspond to Kauffman states of

Some knots in S^1 x S^2 with lens space surgeries

We propose a classification of knots in S^1 x S^2 that admit a longitudinal surgery to a lens space. Any lens space obtainable by longitudinal surgery on some knots in S^1 x S^2 may be obtained from

Lens space surgeries and L-space homology spheres

We describe necessary and sufficient conditions for a knot in an L-space to have an L-space homology sphere surgery. We use these conditions to reformulate a conjecture of Berge about which knots in