Canonical decompositions of 3-manifolds

We describe a new approach to the canonical decompositions of 3-manifolds along tori and annuli due to Jaco-Shalen and Johannson (with ideas from Waldhausen) - the so-called JSJ-decomposition theorem. This approach gives an accessible proof of the decomposition theorem; in particular it does not use the annulus-torus theorems, and the theory of Seifert fibrations does not need to be developed in advance.Comment: 20 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol1/paper3.abs.htm

Corrigendum to "Knot Floer homology detects fibred knots"

We correct a mistake on the citation of JSJ theory in \cite{Ni}. Some arguments in \cite{Ni} are also slightly modified accordingly.Comment: 3 page

Radical Orthodoxy - Panel discussion between Profs Graham Ward, John Milbank, Danie Goosen and Dr Jaco Kruger

No Abstrac

Veering triangulations admit strict angle structures

Agol recently introduced the concept of a veering taut triangulation, which is a taut triangulation with some extra combinatorial structure. We define the weaker notion of a "veering triangulation" and use it to show that all veering triangulations admit strict angle structures. We also answer a question of Agol, giving an example of a veering taut triangulation that is not layered.Comment: 15 pages, 9 figure

Quadrilateral-octagon coordinates for almost normal surfaces

Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional vector space. The quadrilateral coordinates of Tollefson alleviate this problem considerably for normal surfaces, by reducing the dimension of this vector space from 7n to 3n (where n is the complexity of the underlying triangulation). Here we develop an analogous theory for octagonal almost normal surfaces, using quadrilateral and octagon coordinates to reduce this dimension from 10n to 6n. As an application, we show that quadrilateral-octagon coordinates can be used exclusively in the streamlined 3-sphere recognition algorithm of Jaco, Rubinstein and Thompson, reducing experimental running times by factors of thousands. We also introduce joint coordinates, a system with only 3n dimensions for octagonal almost normal surfaces that has appealing geometric properties.Comment: 34 pages, 20 figures; v2: Simplified the proof of Theorem 4.5 using cohomology, plus other minor changes; v3: Minor housekeepin

Re-exploration of vertical rectus abdominis myocutaneous flap for vaginal reconstruction: Case report and review of the literature.

The vertical rectus abdominis myocutaneous (VRAM) flap is a versatile and well-established reconstructive technique for many defects created as a result of colorectal and gynecologic extirpation. However, major re-operation in the pelvis following a VRAM flap reconstruction several months later is uncommon, and the safety and integrity of the VRAM flap in this setting has not been described. This case examines VRAM flap preservation during repeat exploratory laparotomy, and a unique view of the VRAM flap during interval exploration. We demonstrate an intact flap after lysis of adhesions with an audible Doppler signal, and maintenance of flap integrity in the postoperative period. This further substantiates its use as a durable rotational flap for perineal tissue defects

Servant Leadership, Hope Theory, and Future Orientation in Nigerian Agriculture

This original study examined a relationship between the GLOBE Future Orientation (FO) cultural dimension, Hope theory, and Servant Leadership (SL) to influence hope in the Nigerian agricultural industry (House, Hanges, Javidan, Dorfman, & Gupta, 2004). The FO dimension has a solid relationship to the Hope Work construct. Servant Leadership theory should influence the organization, so we asked, can it increase hope in the organization? Three established surveys of hope theory, future orientation, and servant leadership were selected. The selection of participants in Nigeria relied on above high school education level workers at two corporate farms, with 61% being bilingual. The questionnaires were distributed in a convenience sampling to all employees with an above high school educational level present in two corporate farms. The FO measurements indicated that this group was satisfied with the current FO of their organization and did not believe improvements were needed or possible. Both Hope subscales indicate a high ability of the participants to use Hope theory within their organization. The connection between Hope theory and Servant Leadership individual behaviors showed little correlation. However, the finding that all SL behaviors used together demonstrates a strong correlation that can increase hope. Therefore, when all SL behaviors are used together, this recommendation can achieve workplace objectives that increase hope and will be greater than temporal, material gain with the expected results of servant leadership. In conclusion, the use of hope theory to SL behaviors can be an essential addition to improving worker hope in the agricultural industry

Trafficking of cholinesterases and neuroligins mutant proteins. An association with autism

Autism encompasses a wide spectrum of disorders arising during brain development. Recent studies reported that sequence polymorphisms in neuroligin-3 (NLGN3) and neuroligin-4 (NLGN4) genes have been linked to autism spectrum disorders indicating neuroligin genes as candidate targets in brain disorders. We have characterized a single mutation found in two affected brothers that substituted Arg451 to Cys in NL3. Our data show that the exposed Cys causes retention of the protein in the endoplasmic reticulum (ER) when expressed in HEK-293 cells. To examine whether the introduction of a Cys in the C-terminal region of other α/β-hydrolase fold proteins could promote the same cellular phenotype, we made homologous mutations in acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) and found a similar processing deficiency and intracellular retention (De Jaco et al., J Biol Chem. 2006, 281:9667-76). NL3, AChE and BChE mutant proteins are recognized as misfolded in the ER, and degraded via the proteasome pathway. A 2D electrophoresis coupled with mass spectrometry based approach was used to analyze proteins co-immunoprecipitating with NL3 and show differential expression of factors interacting with wild type and mutant NL3. We identified several proteins belonging to distinct ER resident chaperones families, including calnexin, responsible for playing a role in the folding steps of the AChE and NLs. © 2008 Elsevier Ireland Ltd. All rights reserved

Spatial Graphs with Local Knots

It is shown that for any locally knotted edge of a 3-connected graph in $S^3$, there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setwise fixing the graph. This result is applied to the study of topological symmetry groups of graphs embedded in $S^3$.Comment: 20 pages, 3 figures; in v. 2 the proof of Theorem 1 has been clarified, and other minor revisions have been mad