Surgery description of colored knots

The pair (K,r) consisting of a knot K and a surjective map r from the knot group onto a dihedral group is said to be a p-colored knot. D. Moskovich conjectured that for any odd prime p there are exactly p equivalence classes of p-colored knots up to surgery along unknots in the kernel of the coloring. We show that there are at most 2p equivalence classes. This is a vast improvement upon the previous results by Moskovich for p=3, and 5, with no upper bound given in general. T. Cochran, A. Gerges, and K. Orr, in "Dehn surgery equivalence relations of 3-manifolds", define invariants of the surgery equivalence class of a closed 3-manifold M in the context of bordisms. By taking M to be 0-framed surgery of the 3-sphere along K we may define Moskovich's colored untying invariant in the same way as the Cochran-Gerges-Orr invariants. This bordism definition of the colored untying invariant will be then used to establish the upper bound.Comment: 41 pages, 23 figures (Version 3) Minor revisions and typos fixed. Proofs of Propositions 4.1 and 4.8 revise

Half a Million Older Californians Living Alone Unable to Make Ends Meet

Presents findings on the economic security of Californians age 65 and older, using the 2007 Elder Index, with a focus on those living alone. Analyzes data by race/ethnicity, gender, age, and county and compares income levels with the federal poverty line

Included, but Deportable: A New Public Health Approach to Policies That Criminalize and Integrate Immigrants.

There has been a burst of research on immigrant health in the United States and an increasing attention to the broad range of state and local policies that are social determinants of immigrant health. Many of these policies criminalize immigrants by regulating the "legality" of their day-to-day lives while others function to integrate immigrants through expanded rights and eligibility for health care, social services, and other resources.Research on the health impact of policies has primarily focused on the extremes of either criminalization or integration. Most immigrants in the United States, however, live in states that possess a combination of both criminalizing and integrating policies, resulting in distinct contexts that may influence their well-being.We present data describing the variations in criminalization and integration policies across states and provide a framework that identifies distinct but concurrent mechanisms of deportability and inclusion that can influence health. Future public health research and practice should address the ongoing dynamics created by both criminalization and integration policies as these likely exacerbate health inequities by citizenship status, race/ethnicity, and other social hierarchies

Trends in the Health of Older Californians: Data From the 2001, 2003 and 2005 California Health Interview Surveys

Analyzes trends in the health status and use of preventive services among Californians age 65 and over by race/ethnicity, insurance type, and region. Reports rises in doctor visits and in cancer, diabetes, high cholesterol, obesity, and other illnesses

The Elder Economic Security Standard(TM) Index for California, 2007: County Amounts, Comparisons and Components

Provides county-by-county data on how much income retirees need to make ends meet, how it compares with the Federal Poverty Line, and by how much the maximum Supplemental Security Income payment and average Social Security payment each fall short

Surgery description of colored knots

By a knot, or link, we mean a circle, or a collection of circles, embedded in the three-sphere S3. The study of knots is a very rich subject and plays a key role in the area of low-dimensional topology. In fact, a theorem of W.B.R. Lickorish and A.D. Wallace states that any three-dimensional manifold may be described by Dehn surgery along a link which is the process of removing the link from S3 and then gluing it back in a way that possibly changes the resulting manifold. In this dissertation, we will be interested in the pair (K, ρ) consisting of a knot K and a surjective map ρ from the knot group onto a dihedral group of order 2p called a coloring. Such an object is said to be a p-colored knot. In Surgery untying of colored knots , D. Moskovich conjectures that for any odd prime p there are exactly p equivalence classes of p-colored knots up to surgery which preserves colorability. This is an analog to the classical result that every knot has a surgery description or equivalently that every knot is surgery equivalent to the unknot if we place fewer restrictions on the allowed surgery curves. We show that there are at most 2p equivalence classes for p any odd number. This is an improvement upon the previous results by Moskovich for p = 3, and 5, with no upper bound given in general. We do this by defining a new invariant, or an algebraic object associated to a p-colored knot, which is complete in the sense that two p-colored knots are surgery equivalent if and only if they both have the same value of this invariant. The complete invariant consists of Moskovich’s colored untying invariant redefined in the same way as the three-manifold invariants developed by T. Cochran, A. Gerges, and K. Orr, and another object we call the η invariant. We also extend these methods to give similar results for A4-colored knots which have representations onto the alternating group on four letters

Contrasting Inequalities: Comparing Correlates of Health in Canada and the United States

Comparative health studies consistently find that Canadians on average are healthier than Americans. Comparing health status within and between Canada and the United States provides key insights into the distribution of inequalities in these two countries. Canada’s universal health care insurance system contrasts with the mixed system of the United States: universal care for seniors, private health care insurance for many, and no or intermittent coverage for others. These countries are also notably different in the extent of income and racial/ethnic inequalities. It is within this context that this study compares the relative strength of the relationships between social, economic, and demographic factors (sex, age, marital status, income, education, country of birth, and race/ethnicity) and health status in Canada and the United States. Evidence drawn from the 2002-2003 Joint Canada/United States Survey of Health reveals that the correlations between these factors, above all country of birth and race/ethnicity, and health are relatively stronger in the United States, reflecting differences in health care access and racial/ethnic-based inequalities between the countries. The study findings are suggestive of the effects of universal access to health care and more equitable distribution of other social resources in protecting the health of the general population.self-reported health, United States, Canada, health insurance, income, race, ethnicity, age, sex