2 Citations
Property G and the $4$--genus
- Mathematics
- 2020
We say a null-homologous knot $K$ in a $3$--manifold $Y$ has Property G, if the properties about the Thurston norm and fiberedness of the complement of $K$ is preserved under the zero surgery on $K$.…
Null surgery on knots in L-spaces
- Computer Science, ArtTransactions of the American Mathematical Society
- 2019
It is proved that the inline-formula content-type is rationally fibered, that is, the knot complement admits a fibration over the surface bundle over a Dehn surgery to a surface bundle.
References
SHOWING 1-10 OF 40 REFERENCES
Two Applications of Twisted Floer Homology
- Mathematics
- 2008
Given an irreducible closed three-manifold Y, we show that its twisted Heegaard Floer homology determines whether Y is a torus bundle over the circle. Another result we will prove is, if K is a…
Holomorphic discs and sutured manifolds
- Mathematics
- 2006
In this paper we construct a Floer-homology invariant for a natural and wide class of sutured manifolds that we call balanced. This generalizes the Heegaard Floer hat theory of closed three-manifolds…
Holomorphic disks and genus bounds
- Mathematics
- 2004
We prove that, like the Seiberg-Witten monopole homology, the Heegaard Floer homology for a three-manifold determines its Thurston norm. As a consequence, we show that knot Floer homology detects the…
Knot Floer homology and rational surgeries
- Mathematics
- 2010
Let K be a rationally null-homologous knot in a three-manifold Y . We construct a version of knot Floer homology in this context, including a description of the Floer homology of a three-manifold…
Holomorphic disks and three-manifold invariants: Properties and applications
- Mathematics
- 2001
In [27], we introduced Floer homology theories HF - (Y,s), HF∞(Y,s), HF + (Y, t), HF(Y,s),and HF red (Y, s) associated to closed, oriented three-manifolds Y equipped with a Spiny structures s ∈ Spin…
Floer homology and knot complements
- Mathematics
- 2003
We use the Ozsvath-Szabo theory of Floer homology to define an invariant of knot complements in three-manifolds. This invariant takes the form of a filtered chain complex, which we call CF_r. It…
Heegaard Floer homology and fibred 3-manifolds
- Mathematics
- 2007
<abstract abstract-type="TeX"><p>Given a closed $3$-manifold $Y$, we show that the Heegaard Floer homology determines whether $Y$ fibres over the circle with a fibre of negative Euler characteristic.…
Sutured Heegaard diagrams for knots
- Mathematics
- 2006
We define sutured Heegaard diagrams for null-homologous knots in 3–manifolds. These diagrams are useful for computing the knot Floer homology at the top filtration level. As an application, we give a…