Toroidal and Boundary-Reducing Dehn Fillings

Let M be a simple 3-manifold with a toral boundary component partial_0 M. If Dehn filling M along partial_0 M one way produces a toroidal manifold and Dehn filling M along partial_0 M another way produces a boundary-reducible manifold, then we show that the absolute value of the intersection number on partial_0 M of the two filling slopes is at most two. In the special case that the boundary-reducing filling is actually a solid torus and the intersection number between the filling slopes is two, more is said to describe the toroidal filling.Comment: 12 pp., AmSTeX, 6 figs.[uses epsf], Topology Appl. (to appear

Dehn fillings of large hyperbolic 3-manifolds

Let M be a compact, connected, orientable, hyperbolic 3-manifold whose boundary is a torus and which contains an essential closed surface S. It is conjectured that 5 is an upper bound for the distance between two slopes on ∂M whose associated fillings are not hyperbolic manifolds. In this paper we verify the conjecture when the first Betti number of M is at least 2 by showing that given a pseudo-Anosov mapping class f of a surface and an essential simple closed curve γ in the surface, then 5 is an upper bound for the diameter of the set of integers n for which the composition of f with the nth power of a Dehn twist along γ is not pseudo-Anosov. This sharpens an inequality of Albert Fathi. For large manifolds M of first Betti number 1 we obtain partial results. Set C(S) = {slopes r | ker(π1(S) → π1(M(r))) ≠ {1}}. A singular slope for S is a slope r0 ∈ C(S) such that any other slope in C(S) is at most distance 1 from r0. We prove that the distance between two exceptional filling slopes is at most 5 if either (i) there is a closed essential surface S in M with C(S) finite, or (ii) there are singular slopes r1 ≠ r2 for closed essential surfaces S1, S2 in M

Embedding right-angled Artin groups into graph braid groups

We construct an embedding of any right-angled Artin group $G(\Delta)$ defined by a graph $\Delta$ into a graph braid group. The number of strands required for the braid group is equal to the chromatic number of $\Delta$. This construction yields an example of a hyperbolic surface subgroup embedded in a two strand planar graph braid group.Comment: 8 pages. Final version, appears in Geometriae Dedicata

On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups

We show that the isomorphism problem is solvable in the class of central extensions of word-hyperbolic groups, and that the isomorphism problem for biautomatic groups reduces to that for biautomatic groups with finite centre. We describe an algorithm that, given an arbitrary finite presentation of an automatic group $\Gamma$, will construct explicit finite models for the skeleta of $K(\Gamma,1)$ and hence compute the integral homology and cohomology of $\Gamma$.Comment: 21 pages, 4 figure

Functional Assessment of Disease-Associated Regulatory Variants <i>In Vivo</i> Using a Versatile Dual Colour Transgenesis Strategy in Zebrafish

Disruption of gene regulation by sequence variation in non-coding regions of the genome is now recognised as a significant cause of human disease and disease susceptibility. Sequence variants in cis-regulatory elements (CREs), the primary determinants of spatio-temporal gene regulation, can alter transcription factor binding sites. While technological advances have led to easy identification of disease-associated CRE variants, robust methods for discerning functional CRE variants from background variation are lacking. Here we describe an efficient dual-colour reporter transgenesis approach in zebrafish, simultaneously allowing detailed in vivo comparison of spatio-temporal differences in regulatory activity between putative CRE variants and assessment of altered transcription factor binding potential of the variant. We validate the method on known disease-associated elements regulating SHH, PAX6 and IRF6 and subsequently characterise novel, ultra-long-range SOX9 enhancers implicated in the craniofacial abnormality Pierre Robin Sequence. The method provides a highly cost-effective, fast and robust approach for simultaneously unravelling in a single assay whether, where and when in embryonic development a disease-associated CRE-variant is affecting its regulatory function

A cyclic universe with colour fields

The topology of the universe is discussed in relation to the singularity problem. We explore the possibility that the initial state of the universe might have had a structure with 3-Klein bottle topology, which would lead to a model of a nonsingular oscillating (cyclic) universe with a well-defined boundary condition. The same topology is assumed to be intrinsic to the nature of the hypothetical primitive constituents of matter (usually called preons) giving rise to the observed variety of elementary particles. Some phenomenological implications of this approach are also discussed.Comment: 21 pages, 9 figures; v.4: final versio

Distinct Pathogenesis and Host Responses during Infection of C. elegans by P. aeruginosa and S. aureus

The genetically tractable model host Caenorhabditis elegans provides a valuable tool to dissect host-microbe interactions in vivo. Pseudomonas aeruginosa and Staphylococcus aureus utilize virulence factors involved in human disease to infect and kill C. elegans. Despite much progress, virtually nothing is known regarding the cytopathology of infection and the proximate causes of nematode death. Using light and electron microscopy, we found that P. aeruginosa infection entails intestinal distention, accumulation of an unidentified extracellular matrix and P. aeruginosa-synthesized outer membrane vesicles in the gut lumen and on the apical surface of intestinal cells, the appearance of abnormal autophagosomes inside intestinal cells, and P. aeruginosa intracellular invasion of C. elegans. Importantly, heat-killed P. aeruginosa fails to elicit a significant host response, suggesting that the C. elegans response to P. aeruginosa is activated either by heat-labile signals or pathogen-induced damage. In contrast, S. aureus infection causes enterocyte effacement, intestinal epithelium destruction, and complete degradation of internal organs. S. aureus activates a strong transcriptional response in C. elegans intestinal epithelial cells, which aids host survival during infection and shares elements with human innate responses. The C. elegans genes induced in response to S. aureus are mostly distinct from those induced by P. aeruginosa. In contrast to P. aeruginosa, heat-killed S. aureus activates a similar response as live S. aureus, which appears to be independent of the single C. elegans Toll-Like Receptor (TLR) protein. These data suggest that the host response to S. aureus is possibly mediated by pathogen-associated molecular patterns (PAMPs). Because our data suggest that neither the P. aeruginosa nor the S. aureus–triggered response requires canonical TLR signaling, they imply the existence of unidentified mechanisms for pathogen detection in C. elegans, with potentially conserved roles also in mammals