1,695 research outputs found
Comparing invariants of Legendrian knots
We prove the equivalence of the invariants EH(L) and LOSS-(L) for oriented
Legendrian knots L in the 3-sphere equipped with the standard contact
structure, partially extending a previous result by Stipsicz and Vertesi. In
the course of the proof we relate the sutured Floer homology groups associated
with a knot complement and knot Floer homology, and define intermediate
Legendrian invariants.Comment: 30 pages, 9 figures. arXiv admin note: text overlap with
arXiv:1201.528
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
Heegaard Floer homology and concordance bounds on the Thurston norm
We prove that twisted correction terms in Heegaard Floer homology provide
lower bounds on the Thurston norm of certain cohomology classes determined by
the strong concordance class of a 2-component link in . We then
specialise this procedure to knots in , and obtain a lower bound
on their geometric winding number. Furthermore we produce an obstruction for a
knot in to have untwisting number 1. We then provide an infinite family
of null-homologous knots with increasing geometric winding number, on which the
bound is sharp.Comment: With an appendix with Adam Simon Levine; 24 pages, 8 figures;
comments welcome! V2: Fixed a few typos, wrong citations and figures, removed
a proposition. This version to appear in Transactions of the AM
Heegaard Floer correction terms, with a twist
We use Heegaard Floer homology with twisted coefficients to define numerical
invariants for arbitrary closed 3-manifolds equipped torsion spin
structures, generalising the correction terms (or --invariants) defined by
Ozsv\'ath and Szab\'o for integer homology 3-spheres and, more generally, for
3-manifolds with standard . Our twisted correction terms share
many properties with their untwisted analogues. In particular, they provide
restrictions on the topology of 4-manifolds bounding a given 3-manifold.Comment: 24 pages, 2 figures; New proof of additivity (Proposition 3.7) based
on a connected sum formula for twisted coefficients (Proposition 2.3);
exposition improved, mainly in Section 4; Proposition 3.8 downgraded to an
inequality due to an error in the previous version found by Adam Levin
Pair of pants decomposition of 4-manifolds
Using tropical geometry, Mikhalkin has proved that every smooth complex
hypersurface in decomposes into pairs of pants: a pair of
pants is a real compact -manifold with cornered boundary obtained by
removing an open regular neighborhood of generic hyperplanes from
. As is well-known, every compact surface of genus decomposes into pairs of pants, and it is now natural to investigate this
construction in dimension 4. Which smooth closed 4-manifolds decompose into
pairs of pants? We address this problem here and construct many examples: we
prove in particular that every finitely presented group is the fundamental
group of a 4-manifold that decomposes into pairs of pants.Comment: 41 pages, 25 figures; exposition has been improved; the proof of
Theorem 2 was incorrect, and it has been fixed. Accepted for publications in
Algebr. Geom. Topo
Nearly AdS2 Sugra and the Super-Schwarzian
In nearly AdS2 gravity the Einstein-Hilbert term is supplemented by the
Jackiw-Teitelboim action. Integrating out the bulk metric gives rise to the
Schwarzian action for the boundary curve. In the present note, we show how the
extension to supergravity leads to the super-Schwarzian action for the
superspace boundary.Comment: 10 pages, v2: minor error corrected, references added,v3: more
references added, accepted for publicatio
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