Universal manifold pairings and positivity

Gluing two manifolds M_1 and M_2 with a common boundary S yields a closed manifold M. Extending to formal linear combinations x=Sum_i(a_i M_i) yields a sesquilinear pairing p= with values in (formal linear combinations of) closed manifolds. Topological quantum field theory (TQFT) represents this universal pairing p onto a finite dimensional quotient pairing q with values in C which in physically motivated cases is positive definite. To see if such a "unitary" TQFT can potentially detect any nontrivial x, we ask if is non-zero whenever x is non-zero. If this is the case, we call the pairing p positive. The question arises for each dimension d=0,1,2,.... We find p(d) positive for d=0,1, and 2 and not positive for d=4. We conjecture that p(3) is also positive. Similar questions may be phrased for (manifold, submanifold) pairs and manifolds with other additional structure. The results in dimension 4 imply that unitary TQFTs cannot distinguish homotopy equivalent simply connected 4-manifolds, nor can they distinguish smoothly s-cobordant 4-manifolds. This may illuminate the difficulties that have been met by several authors in their attempts to formulate unitary TQFTs for d=3+1. There is a further physical implication of this paper. Whereas 3-dimensional Chern-Simons theory appears to be well-encoded within 2-dimensional quantum physics, eg in the fractional quantum Hall effect, Donaldson-Seiberg-Witten theory cannot be captured by a 3-dimensional quantum system. The positivity of the physical Hilbert spaces means they cannot see null vectors of the universal pairing; such vectors must map to zero.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper53.abs.htm

A Novel Mutation in the Upstream Open Reading Frame of the CDKN1B Gene Causes a MEN4 Phenotype

PubMed ID: 23555276This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Aging, Retirement, and Changes in Physical Activity: Prospective Cohort Findings from the GLOBE Study

There is increased recognition that determinants of health should be investigated in a life-course perspective. Retirement is a major transition in the life course and offers opportunities for changes in physical activity that may improve health in the aging population. The authors examined the effect of retirement on changes in physical activity in the GLOBE Study, a prospective cohort study known by the Dutch acronym for "Health and Living Conditions of the Population of Eindhoven and surroundings," 1991–2004. They followed respondents (n = 971) by postal questionnaire who were employed and aged 40–65 years in 1991 for 13 years, after which they were still employed (n = 287) or had retired (n = 684). Physical activity included 1) work-related transportation, 2) sports participation, and 3) nonsports leisure-time physical activity. Multinomial logistic regression analyses indicated that retirement was associated with a significantly higher odds for a decline in physical activity from work-related transportation (odds ratio (OR) = 3.03, 95% confidence interval (CI): 1.97, 4.65), adjusted for sex, age, marital status, chronic diseases, and education, compared with remaining employed. Retirement was not associated with an increase in sports participation (OR = 1.12, 95% CI: 0.71, 1.75) or nonsports leisure-time physical activity (OR = 0.80, 95% CI: 0.54, 1.19). In conclusion, retirement introduces a reduction in physical activity from work-related transportation that is not compensated for by an increase in sports participation or an increase in nonsports leisure-time physical activity