73 research outputs found
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
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
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
Open book decompositions versus prime factorizations of closed, oriented 3-manifolds
Let be a closed, oriented, connected 3--manifold and an open
book decomposition on with page and monodromy . It is
easy to see that the first Betti number of is bounded below by the
number of --factors in the prime factorization of . Our main
result is that equality is realized if and only if is trivial and
is a connected sum of 's. We also give some applications of our
main result, such as a new proof of the result by Birman and Menasco that if
the closure of a braid with strands is the unlink with components then
the braid is trivial.Comment: 8 pages, 1 figure. Submitted to the proceedings of the conference
"Interactions between low dimensional topology and mapping class groups",
July 1-5, 2013, Max Planck Institute for Mathematics, Bon
On Stein fillings of contact torus bundles
We consider a large family F of torus bundles over the circle, and we use
recent work of Li--Mak to construct, on each Y in F, a Stein fillable contact
structure C. We prove that (i) each Stein filling of (Y,C) has vanishing first
Chern class and first Betti number, (ii) if Y in F is elliptic then all Stein
fillings of (Y,C) are pairwise diffeomorphic and (iii) if Y in F is parabolic
or hyperbolic then all Stein fillings of (Y,C) share the same Betti numbers and
fall into finitely many diffeomorphism classes. Moreover, for infinitely many
hyperbolic torus bundles Y in F we exhibit non-homotopy equivalent Stein
fillings of (Y,C).Comment: 18 pages, 10 figures. This preprint version differs from the final
version which is to appear in the Bulletin of the London Mathematical Societ
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
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
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