Tight contact structures and genus one fibered knots

We study contact structures compatible with genus one open book decompositions with one boundary component. Any monodromy for such an open book can be written as a product of Dehn twists around dual non-separating curves in the once-punctured torus. Given such a product, we supply an algorithm to determine whether the corresponding contact structure is tight or overtwisted. We rely on Ozsv{\'a}th-Szab{\'o} Heegaard Floer homology in our construction and, in particular, we completely identify the $L$-spaces with genus one, one boundary component, pseudo-Anosov open book decompositions. Lastly, we reveal a new infinite family of hyperbolic three-manifolds with no co-orientable taut foliations, extending the family discovered in \cite{RSS}.Comment: 30 pages, 10 figures. Added figures, extended result to all monodromies, and added sections 5 and

On Three-Dimensional Space Groups

An entirely new and independent enumeration of the crystallographic space groups is given, based on obtaining the groups as fibrations over the plane crystallographic groups, when this is possible. For the 35 ``irreducible'' groups for which it is not, an independent method is used that has the advantage of elucidating their subgroup relationships. Each space group is given a short ``fibrifold name'' which, much like the orbifold names for two-dimensional groups, while being only specified up to isotopy, contains enough information to allow the construction of the group from the name.Comment: 26 pages, 8 figure

Classifying closed 2-orbifolds with Euler characteristics

We determine the extent to which the collection of $\Gamma$-Euler-Satake characteristics classify closed 2-orbifolds. In particular, we show that the closed, connected, effective, orientable 2-orbifolds are classified by the collection of $\Gamma$-Euler-Satake characteristics corresponding to free or free abelian $\Gamma$ and are not classified by those corresponding to any finite collection of finitely generated discrete groups. Similarly, we show that such a classification is not possible for non-orientable 2-orbifolds and any collection of $\Gamma$, nor for noneffective 2-orbifolds. As a corollary, we generate families of orbifolds with the same $\Gamma$-Euler-Satake characteristics in arbitrary dimensions for any finite collection of $\Gamma$; this is used to demonstrate that the $\Gamma$-Euler-Satake characteristics each constitute new invariants of orbifolds.Comment: 17 page

Voyages

Susanna Moodie is, of course, best known for her books Roughing It in the Bush and Life in the Clearings, which are largely comprised of short sketches that she had previously published. What is not widely known, however, is that Moodie had a long and prolific literary career in which short sketches and tales were among her favoured genres. This book offers a selection of these narratives, most of which have been unavailable in print since the 19th century. This collection will give the reader a new understanding of Susanna Moodie's work

Closed surface bundles of least volume

Since the set of volumes of hyperbolic 3-manifolds is well ordered, for each fixed g there is a genus-g surface bundle over the circle of minimal volume. Here, we introduce an explicit family of genus-g bundles which we conjecture are the unique such manifolds of minimal volume. Conditional on a very plausible assumption, we prove that this is indeed the case when g is large. The proof combines a soft geometric limit argument with a detailed Neumann-Zagier asymptotic formula for the volumes of Dehn fillings. Our examples are all Dehn fillings on the sibling of the Whitehead manifold, and we also analyze the dilatations of all closed surface bundles obtained in this way, identifying those with minimal dilatation. This gives new families of pseudo-Anosovs with low dilatation, including a genus 7 example which minimizes dilatation among all those with orientable invariant foliations.Comment: 22 pages, 4 figures. V2: Corrected Table 1.9; V3: Added Table 1.10; V4: Minor edits; V5: Corrected Figure 2.1. To appear in AG&

Mainstreaming prevention: Prescribing fruit and vegetables as a brief intervention in primary care

This is the author's PDF version of an article published in Public health© 2005.This articles discusses a project at the Castlefields Health Centre in Halton whereby primary care professionals issue a prescription for discounts on fruit and vegetables. The prescription is explicitly linked to the five-a-day message

Preparation and Characterization of Photoactive Antimicrobial Graphitic Carbon Nitride (g-C\u3csub\u3e3\u3c/sub\u3eN\u3csub\u3e4\u3c/sub\u3e) Films

Photoactive films derived from nanostructured samples of the metal-free, intermediate band gap semiconductor graphitic carbon nitride (ns-g-C3N4) have been synthesized and characterized for their particle properties and antimicrobial activity. Physical characterization reveals that these materials are composed of discrete nanoparticles whose dimensions range from 200 nm to 700 nm. Investigation of the photochemical reactivity of ns-g-C3N4 using coumarin-3- carboxylic acid (3-CCA) indicates that this material produces reactive oxygen species (ROS) under visible radiation. When irradiated with 0.31J visible light, ns-g-C3N4-based materials reduced the viability of both gram-negative Escherichia coli O157:H7 and gram-positive Staphylococcus aureus by approximately 50%. Nearly complete inactivation of both strains of microorganisms was achieved upon administration of a 0.62J dose of visible radiation. Importantly, no biocidal activity was observed for non-irradiated samples, indicating that the g-C3N4-derived films are not inherently toxic in the absence of visible light. The results of this study suggest that materials and, by extention, films and coatings derived from g-C3N4 may present a novel route for controlling pathogenic microorganisms on surfaces in the environment, and could be useful in reducing incidents of hospital-acquired infections

ODELAY: A Large-scale Method for Multi-parameter Quantification of Yeast Growth.

Growth phenotypes of microorganisms are a strong indicator of their underlying genetic fitness and can be segregated into 3 growth regimes: lag-phase, log-phase, and stationary-phase. Each growth phase can reveal different aspects of fitness that are related to various environmental and genetic conditions. High-resolution and quantitative measurements of all 3 phases of growth are generally difficult to obtain. Here we present a detailed method to characterize all 3 growth phases on solid media using an assay called One-cell Doubling Evaluation of Living Arrays of Yeast (ODELAY). ODELAY quantifies growth phenotypes of individual cells growing into colonies on solid media using time-lapse microscopy. This method can directly observe population heterogeneity with each growth parameter in genetically identical cells growing into colonies. This population heterogeneity offers a unique perspective for understanding genetic and epigenetic regulation, and responses to genetic and environmental perturbations. While the ODELAY method is demonstrated using yeast, it can be utilized on any colony forming microorganism that is visible by bright field microscopy

The Copernican Principle in Compact Spacetimes

Copernicus realised we were not at the centre of the universe. A universe made finite by topological identifications introduces a new Copernican consideration: while we may not be at the geometric centre of the universe, some galaxy could be. A finite universe also picks out a preferred frame: the frame in which the universe is smallest. Although we are not likely to be at the centre of the universe, we must live in the preferred frame (if we are at rest with respect to the cosmological expansion). We show that the preferred topological frame must also be the comoving frame in a homogeneous and isotropic cosmological spacetime. Some implications of topologically identifying time are also discussed.Comment: 5 page