## One Citation

### On Floer minimal knots in sutured manifolds

- Computer ScienceTransactions of the American Mathematical Society, Series B
- 2022

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="http://www.w3.org/1998/Math/MathML" alttext="upper M">.

## References

SHOWING 1-10 OF 25 REFERENCES

### Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology

- Mathematics
- 2008

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

- Mathematics
- 2010

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

- Mathematics
- 2007

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…

### The lens space realization problem

- Mathematics
- 2010

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

- Mathematics
- 2013

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

- Mathematics
- 2013

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

- Mathematics
- 2007

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…