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

3-manifolds which are spacelike slices of flat spacetimes

We continue work initiated in a 1990 preprint of Mess giving a geometric parameterization of the moduli space of classical solutions to Einstein's equations in 2+1 dimensions with cosmological constant 0 or -1 (the case +1 has been worked out in the interim by the present author). In this paper we make a first step toward the 3+1-dimensional case by determining exactly which closed 3-manifolds M^3 arise as spacelike slices of flat spacetimes, and by finding all possible holonomy homomorphisms pi_1(M^3) to ISO(3,1).Comment: 10 page

Homogeneous links, Seifert surfaces, digraphs and the reduced Alexander polynomial

We give a geometric proof of the following result of Juhasz. \emph{Let $a_g$ be the leading coefficient of the Alexander polynomial of an alternating knot $K$. If $|a_g|<4$ then $K$ has a unique minimal genus Seifert surface.} In doing so, we are able to generalise the result, replacing `minimal genus' with `incompressible' and `alternating' with `homogeneous'. We also examine the implications of our proof for alternating links in general.Comment: 37 pages, 28 figures; v2 Main results generalised from alternating links to homogeneous links. Title change

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

Decoupling Inflation From the String Scale

When Inflation is embedded in a fundamental theory, such as string theory, it typically begins when the Universe is already substantially larger than the fundamental scale [such as the one defined by the string length scale]. This is naturally explained by postulating a pre-inflationary era, during which the size of the Universe grew from the fundamental scale to the initial inflationary scale. The problem then arises of maintaining the [presumed] initial spatial homogeneity throughout this era, so that, when it terminates, Inflation is able to begin in its potential-dominated state. Linde has proposed that a spacetime with compact negatively curved spatial sections can achieve this, by means of chaotic mixing. Such a compactification will however lead to a Casimir energy, which can lead to effects that defeat the purpose unless the coupling to gravity is suppressed. We estimate the value of this coupling required by the proposal, and use it to show that the pre-inflationary spacetime is stable, despite the violation of the Null Energy Condition entailed by the Casimir energy.Comment: 24 pages, 5 eps figures, references added, stylistic changes, version to appear in Classical and Quantum Gravit