Complements of tori and Klein bottles in the 4-sphere that have hyperbolic structure

Many noncompact hyperbolic 3-manifolds are topologically complements of links in the 3-sphere. Generalizing to dimension 4, we construct a dozen examples of noncompact hyperbolic 4-manifolds, all of which are topologically complements of varying numbers of tori and Klein bottles in the 4-sphere. Finite covers of some of those manifolds are then shown to be complements of tori and Klein bottles in other simply-connected closed 4-manifolds. All the examples are based on a construction of Ratcliffe and Tschantz, who produced 1171 noncompact hyperbolic 4-manifolds of minimal volume. Our examples are finite covers of some of those manifolds.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-41.abs.htm

F and D Values with Explicit Flavor Symmetry Breaking and \Delta s Contents of Nucleons

We propose a new model for describing baryon semi-leptonic decays for estimating $F$ and $D$ values with explicit breaking effects of both SU(3) and SU(2) flavor symmetry, where all possible SU(3) and SU(2) breaking effects are induced from an effective interaction. An overall fit including the weak magnetism form factor yields $F=0.477\pm 0.001$ and $D=0.835\pm 0.001$ with $\chi^2=4.43/5$ d.o.f. with $V_{ud}=0.975\pm 0.002$ and $V_{us}=0.221\pm 0.002$. The spin content of strange quarks $\Delta s$ is estimated from the obtained values $F$ and $D$, and the nucleon spin problem is re-examined. Furthermore, the unmeasured values of $(g_1/f_1)$ and $(g_1)$ for other hyperon semi-leptonic decays are predicted from this new formula.Comment: 15 pages, 1 figure, final version to appear in PR

Salem numbers and arithmetic hyperbolic groups

In this paper we prove that there is a direct relationship between Salem numbers and translation lengths of hyperbolic elements of arithmetic hyperbolic groups that are determined by a quadratic form over a totally real number field. As an application we determine a sharp lower bound for the length of a closed geodesic in a noncompact arithmetic hyperbolic n-orbifold for each dimension n. We also discuss a "short geodesic conjecture", and prove its equivalence with "Lehmer's conjecture" for Salem numbers.Comment: The exposition in version 3 is more compact; this shortens the paper: 26 pages now instead of 37. A discussion on Lehmer's problem has been added in Section 1.2. Final version, to appear is Trans. AM

Older people, regeneration and health and well-being. Case study of Salford Partnership Board for Older People

This study sat within a national project aimed at demonstrating that expert knowledge housed within universities can make a positive impact in urban communities around four themes: Community Cohesion, Crime, Enterprise and Health & Wellbeing. It involved the Universities of Salford, Northumbria, Central Lancashire, Manchester Metropolitan University and Bradford. The project aimed to address key urban regeneration challenges in the North of England through inter-disciplinary collaboration between partner universities and practitioner organisations. It also sought to build a long term strategic alliance between core university partners. Within each of the four project areas there were a number of smaller projects each focusing on the relationship between the theme and urban regeneration. This study sought to establish how partnership boards for older people address the health and well being needs of people over 50 years of age including how health and wellbeing are defined; strategies older people adopt to change service providers' actions; learning by service providers about the involvement of older people on Boards; and how this influences practice. The main activity within this study was to interview Salford Partnership Board members. The findings informed further development of the Board