Knot Floer homology detects fibred knots

Ozsv\'ath and Szab\'o conjectured that knot Floer homology detects fibred knots in $S^3$. We will prove this conjecture for null-homologous knots in arbitrary closed 3--manifolds. Namely, if $K$ is a knot in a closed 3--manifold $Y$, $Y-K$ is irreducible, and $\hat{HFK}(Y,K)$ is monic, then $K$ is fibred. The proof relies on previous works due to Gabai, Ozsv\'ath--Szab\'o, Ghiggini and the author. A corollary is that if a knot in $S^3$ admits a lens space surgery, then the knot is fibred.Comment: version 4: incorporates referee's suggestions, to appear in Inventiones Mathematica

Virtual Betti numbers of genus 2 bundles

We show that if M is a surface bundle over S^1 with fiber of genus 2, then for any integer n, M has a finite cover tilde(M) with b_1(tilde(M)) > n. A corollary is that M can be geometrized using only the `non-fiber' case of Thurston's Geometrization Theorem for Haken manifolds.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper19.abs.htm

Promoting Essential Laminations

We show that every co--orientable taut foliation F of an orientable, atoroidal 3-manifold admits a transverse essential lamination. If this transverse lamination is a foliation G, the pair F,G are the unstable and stable foliation respectively of an Anosov flow. Otherwise, F admits a pair of transverse very full genuine laminations. In the second case, M satisfies the weak geometrization conjecture - either its fundamental group contains Z+Z or it is word-hyperbolic. Moreover, if M is atoroidal, the mapping class group of M is finite, and any automorphism homotopic to the identity is isotopic to the identity.Comment: 56 pages, 11 figures; version 3: final version, incorporates referee's suggestion

Thin presentation of knots and lens spaces

This paper concerns thin presentations of knots K in closed 3-manifolds M^3 which produce S^3 by Dehn surgery, for some slope gamma. If M does not have a lens space as a connected summand, we first prove that all such thin presentations, with respect to any spine of M have only local maxima. If M is a lens space and K has an essential thin presentation with respect to a given standard spine (of lens space M) with only local maxima, then we show that K is a 0-bridge or 1-bridge braid in M; furthermore, we prove the minimal intersection between K and such spines to be at least three, and finally, if the core of the surgery K_gamma yields S^3 by r-Dehn surgery, then we prove the following inequality: |r| <= 2g, where g is the genus of K_gamma.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-23.abs.htm

On three-manifolds dominated by circle bundles

We determine which three-manifolds are dominated by products. The result is that a closed, oriented, connected three-manifold is dominated by a product if and only if it is finitely covered either by a product or by a connected sum of copies of the product of the two-sphere and the circle. This characterization can also be formulated in terms of Thurston geometries, or in terms of purely algebraic properties of the fundamental group. We also determine which three-manifolds are dominated by non-trivial circle bundles, and which three-manifold groups are presentable by products.Comment: 12 pages; to appear in Math. Zeitschrift; ISSN 1103-467

Overstocking dairy cows during the dry period affects dehydroepiandrosterone and cortisol secretion

Stressful situations trigger several changes such as the secretion of cortisol and dehydroepiandrosterone (DHEA) from the adrenal cortex, in response to ACTH. The aim of this study was to verify whether overstocking during the dry period (from 21&nbsp;\ub1&nbsp;3 d to the expected calving until calving) affects DHEA and cortisol secretion and behavior in Holstein Friesian cows. Twenty-eight cows were randomly divided into 2 groups (14 animals each), balanced for the number of lactations, body condition score, and expected date of calving. Cows in the far-off phase of the dry period (from 60 to 21 d before the expected calving date) were housed together in a bedded pack. Then, animals from 21&nbsp;\ub1&nbsp;3 d before the expected calving until calving were housed in pens with the same size but under different crowding conditions due to the introduction of heifers (interference animals) into the pen. The control condition (CTR) had 2 animals per pen with 12.0&nbsp;m2 each, whereas the overstocked condition (OS) had 3 interference animals in the same pen with 4.8&nbsp;m2 for each animal. On d 1230&nbsp;\ub1&nbsp;3, 1221&nbsp;\ub1&nbsp;3, 1215&nbsp;\ub1&nbsp;3, 1210&nbsp;\ub1&nbsp;3, and 125&nbsp;\ub1&nbsp;3 before and 10, 20, and 30 after calving, blood samples were collected from each cow for the determination of plasma DHEA and cortisol concentrations by RIA. Rumination time (min/d), activity (steps/h), lying time (min/d), and lying bouts (bouts/d) were individually recorded daily. In both groups, DHEA increased before calving and the concentration declined rapidly after parturition. Overstocking significantly increased DHEA concentration compared with the CTR group at d 1210 (1.79&nbsp;\ub1&nbsp;0.09 vs. 1.24&nbsp;\ub1&nbsp;0.14 pmol/mL), whereas an increase of cortisol was observed at d 1215 (3.64&nbsp;\ub1&nbsp;0.52 vs. 1.64&nbsp;\ub1&nbsp;0.46&nbsp;ng/mL). The OS group showed significantly higher activity (steps/h) compared with the CTR group. Daily lying bouts tended to be higher for the OS group compared with CTR group in the first week of treatment. The overall results of this study documented that overstocking during the dry period was associated with a short-term changes in DHEA and cortisol but these hormonal modifications did not influence cow behavior

Right-veering diffeomorphisms of compact surfaces with boundary II

We continue our study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary, introduced in [HKM2]. We conduct a detailed study of the case when the surface is a punctured torus; in particular, we exhibit the difference between the monoid of right-veering diffeomorphisms and the monoid of products of positive Dehn twists, with the help of the Rademacher function. We then generalize to the braid group B_n on n strands by relating the signature and the Maslov index. Finally, we discuss the symplectic fillability in the pseudo-Anosov case by comparing with the work of Roberts [Ro1,Ro2].Comment: 25 pages, 5 figure