1,409 research outputs found

    Quasi-Isometric Embeddings of Symmetric Spaces

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    We prove a rigidity theorem that shows that, under many circumstances, quasi-isometric embeddings of equal rank, higher rank symmetric spaces are close to isometric embeddings. We also produce some surprising examples of quasi-isometric embeddings of higher rank symmetric spaces. In particular, we produce embeddings of SL(n,R)SL(n,\mathbb R) into Sp(2(n−1),R)Sp(2(n-1),\mathbb R) when no isometric embeddings exist. A key ingredient in our proofs of rigidity results is a direct generalization of the Mostow-Morse Lemma in higher rank. Typically this lemma is replaced by the quasi-flat theorem which says that maximal quasi-flat is within bounded distance of a finite union of flats. We improve this by showing that the quasi-flat is in fact flat off of a subset of codimension 22.Comment: Exposition improved, outlines of proofs added to introduction. Typos corrected, references added. Also some discussion of the reducible case adde

    Alcohol-related mortality in deprived UK cities: worrying trends in young women challenge recent national downward trends

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    Background: Glasgow, the largest city in Scotland, has high levels of deprivation and a poor-health profile compared with other parts of Europe, which cannot be fully explained by the high levels of deprivation. The ‘excess’ premature mortality in Glasgow is now largely attributable to deaths from alcohol, drugs, suicide and violence. Methods: Alcohol-related mortality in Glasgow from 1980 to 2011 was examined relative to the equally deprived UK cities of Manchester and Liverpool with the aim of identifying differences across the cities, with respect to gender, age and birth cohort, that could help explain the ‘excess’ mortality in Glasgow. Results: In the 1980s, alcohol-related mortality in Glasgow was three times higher than in Manchester and Liverpool. Alcohol-related mortality increased in all three cities over the subsequent three decades, but a sharp rise in deaths in the early 1990s was unique to Glasgow. The increase in numbers of deaths in Glasgow was greater than in Manchester and Liverpool, but there was little difference in the pattern of alcohol-related deaths, by sex or birth cohort that could explain the excess mortality in Glasgow. The recent modest decrease in alcohol-related mortality was largely experienced by all birth cohorts, with the notable exception of the younger cohort (born between 1970 and 1979): women in this cohort across all three cities experienced disproportionate increases in alcohol-related mortality. Conclusions: It is imperative that this early warning sign in young women in the UK is acted on if deaths from alcohol are to reduce in the long term

    Coarse differentiation of quasi-isometries II: Rigidity for Sol and Lamplighter groups

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    In this paper, which is the continuation of [EFW2], we complete the proof of the quasi-isometric rigidity of Sol and the lamplighter groups. The results were announced in [EFW1].Comment: 47 pages, 3 figures. Minor revisions addressing comments by the refere

    Coarse differentiation of quasi-isometries I: spaces not quasi-isometric to Cayley graphs

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    In this paper, we prove that certain spaces are not quasi-isometric to Cayley graphs of finitely generated groups. In particular, we answer a question of Woess and prove a conjecture of Diestel and Leader by showing that certain homogeneous graphs are not quasi-isometric to a Cayley graph of a finitely generated group. This paper is the first in a sequence of papers proving results announced in [EFW0]. In particular, this paper contains many steps in the proofs of quasi-isometric rigidity of lattices in Sol and of the quasi-isometry classification of lamplighter groups. The proofs of those results are completed in [EFW1]. The method used here is based on the idea of "coarse differentiation" introduced in [EFW0].Comment: 44 pages; 4 figures; minor corrections addressing comments by the refere

    Has Scotland always been the ‘sick man’ of Europe? An observational study from 1855 to 2006

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    Background: Scotland has been dubbed ‘the sick man of Europe’ on account of its higher mortality rates compared with other western European countries. It is not clear the length of time for which Scotland has had higher mortality rates. The root causes of the higher mortality in Scotland remain elusive. Methods: Life expectancy data from the Human Mortality Database were tabulated and graphed for a selection of wealthy, mainly European countries from around 1850 onwards. Results: Scotland had a life expectancy in the mid-range of countries included in the Human Mortality Database from the mid-19th century until around 1950. After 1950, Scottish life expectancy improved at a slower rate than in comparably wealthy nations before further faltering during the last 30 years. Scottish life expectancy now lies between that of western European and eastern European nations. The USA also displays a marked faltering in its life expectancy trend after 1981. There is an inverse association between life expectancy and the Index of Economic Freedom such that greater neoliberalism is associated with a smaller increase, or a decrease, in life expectancy. Conclusion: Life expectancy in Scotland has only been relatively low since around 1950. From 1980, life expectancy in Scotland, the USA and, to a greater extent, the former USSR displays a further relative faltering. It has been suggested that Scotland suffered disproportionately from the adoption of neoliberalism across the nations of the UK, and the evidence here both supports this suggestion and highlights other countries which may have suffered similarly

    Non-resident Fathers: A Literature Review of Factors Influencing their World

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    It has been acknowledged (McCashin, 1996; Hogan & Gilbertson, 2007) that services designed to support families tend to focus on the mother and children and little contact is generally made with fathers, even when they are resident in the family home. Considering the changes in family structure in contemporary society and the often complex range of needs held by families who avail of social care services, this paper provides some insights in the factors that impact on non-resident fathers. The paper presents a literature review on the topic of non-resident fathers covering areas such as fathers’ role in the family and in children’s development; factors that have been found to impact on non-resident fathers’ contact with their children and the impact of non-residency on the fathers themselves
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