On overtwisted, right-veering open books

We exhibit infinitely many overtwisted, right-veering, non-destabilizable open books, thus providing infinitely many counterexamples to a conjecture of Honda-Kazez-Matic. The page of all our open books is a four-holed sphere and the underlying 3-manifolds are lens spaces.Comment: 6 pages, 4 figures. v2: minor edits, accepted for publication in the Pacific Journal of Mathematic

Contact surgery and transverse invariants

We derive new existence results for tight contact structures on certain 3-manifolds which can be presented as surgery along specific knots in S^3. Indeed, we extend our earlier results on knots with maximal Thurston-Bennequin number being equal to 2g-1 to knots for which the maximal self-linking number satisfies the same equality. In the argument (using contact surgery) we define an invariant for transverse knots in contact 3-manifolds under the assumption that either the knot is null-homologous or the 3-manifold has no S^1xS^2-factor in its prime decomposition, and we study its properties using the Ozsvath-Szabo contact invariant.Comment: 25 pages, 8 figures. Text and figures slightly edited. Accepted for publication by the Journal of Topolog

On 3-braid knots of finite concordance order

We study 3-braid knots of finite smooth concordance order. A corollary of our main result is that a chiral 3-braid knot of finite concordance order is ribbon.Comment: To appear in Transactions of the American Mathematical Society. 25 pages, 4 figure

Sums of lens spaces bounding rational balls

We classify connected sums of three-dimensional lens spaces which smoothly bound rational homology balls. We use this result to determine the order of each lens space in the group of rational homology 3-spheres up to rational homology cobordisms, and to determine the concordance order of each 2-bridge knot.Comment: 20 pages, 4 figure

Signatures, Heegaard Floer correction terms and quasi-alternating links

Turaev showed that there is a well-defined map assigning to an oriented link L in the three-sphere a Spin structure t_0 on Sigma(L), the 2-fold cover of S^3 branched along L. We prove, generalizing results of Manolescu-Owens and Donald-Owens, that for an oriented quasi-alternating link L the signature of L equals minus four times the Heegaard Floer correction term of (Sigma(L), t_0).Comment: V2: Improved exposition incorporating referee's suggestions; 3 figures, 6 pages. Accepted for publication by the Proceedings of the American Mathematical Societ