83 research outputs found
Gluck twist on a certain family of 2-knots
We show that by performing the Gluck twist along the 2-knot
derived from two ribbon presentations of the ribbon 1-knot we get the
standard 4-sphere . In the proof we apply Kirby calculus.Comment: 11 pages, 12 figure
On the μ invariant of rational surface singularities
We show that for rational surface singularities with odd deter-
minant the μ invariant defined by W. Neumann is an obstruction for the
link of the singularity to bound a rational homology 4–ball. We identify
the μ invariant with the corresponding correction term in Heegaard Floer
theory
On invariants for Legendrian knots
Suppose that L is a null--homologous Legendrian knot in a contact
3--manifold. We determine the connection between the sutured invariant of the
complement of L and the Legendrian invariant defined by Lisca, Ozsvath,
Stipsicz and Szabo. In particular, we derive a vanishing theorem for the
Legendrian invariant in the presence of Giroux torsion in the complement of the
knot, and reprove several known properties of the Legendrian invariant from
this perspective.Comment: 19 pages, 11 figure
Combinatorial Heegaard Floer homology and sign assignments
We provide an intergral lift of the combinatorial definition of Heegaard
Floer homology for nice diagrams, and show that the proof of independence using
convenient diagrams adapts to this setting.Comment: 51 pages, 32 figure
- …