Gluck twist on a certain family of 2-knots

We show that by performing the Gluck twist along the 2-knot $K^2_{pq}$ derived from two ribbon presentations of the ribbon 1-knot $K(p,q)$ we get the standard 4-sphere $S^4$. 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