A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture

Doing surgery on the 5-torus, we construct a 5-dimensional closed spin-manifold M with $\pi_1(M) = Z^4times Z/3$, so that the index invariant in the KO-theory of the reduced $C^*$-algebra of $\pi_1(M)$ is zero. Then we use the theory of minimal surfaces of Schoen/Yau to show that this manifolds cannot carry a metric of positive scalar curvature. The existence of such a metric is predicted by the (unstable) Gromov-Lawson-Rosenberg conjecture.Comment: 4 pages, ol

Equivariant Euler characteristics and K-homology Euler classes for proper cocompact G-manifolds

Let G be a countable discrete group and let M be a smooth proper cocompact G-manifold without boundary. The Euler operator defines via Kasparov theory an element, called the equivariant Euler class, in the equivariant K-homology of M. The universal equivariant Euler characteristic of M, which lives in a group U^G(M), counts the equivariant cells of M, taking the component structure of the various fixed point sets into account. We construct a natural homomorphism from U^G(M) to the equivariant KO-homology of M. The main result of this paper says that this map sends the universal equivariant Euler characteristic to the equivariant Euler class. In particular this shows that there are no `higher' equivariant Euler characteristics. We show that, rationally, the equivariant Euler class carries the same information as the collection of the orbifold Euler characteristics of the components of the L-fixed point sets M^L, where L runs through the finite cyclic subgroups of G. However, we give an example of an action of the symmetric group S_3 on the 3-sphere for which the equivariant Euler class has order 2, so there is also some torsion information.Comment: Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper16.abs.htm

Child Care Subsidies in the Mid-Hudson Valley: An Analysis of Need, Availability and Trends

Child care is an enormous expense for families with working parents, especially those with young children not yet in school and low incomes. For example, according to New York State, a family needing full-time care for an infant under 18 months that selects a day care center can expect to pay as much as $252 a week, or nearly$13,100 a year.1 That comes close to consuming the entire paycheck of a minimum-wage worker, who will earn (before taxes) $16,640 in a year. The child care subsidy program operated by counties in New York State aims to ease that burden, helping to keep parents in the workforce and provide access to high quality care for their children. Yet in most parts of New York State, subsidies have become less available over the past several years. From 2007 to 2013, the number of subsidies dropped in 38 of New York's 57 counties outside New York City, with an average decline of 27%. CGR and the Greater Rochester League of Women Voters chose child care subsidies as the focus of our annual research effort in 2014, funded out of the Beatrice Bibby Endowment. We received additional support to conduct in-depth analyses of the Mid-Hudson Valley and Long Island from the Dyson and Rauch Foundations. This report examines availability, need, funding and policies related to child care subsidies in the Mid-Hudson Valley and New York State as a whole

Changes in the phytoplankton

An article discussing changes observed in phytoplankton of the Lake District. An overview is given of previous phytoplankton studies undertaken in the area, detailing some changes found in various waterbodies. Water quality changes in Lake Windermere are mentioned, including the gradual increase of dissolved organic matter (DOM), believed to be caused by the increase of sewage to the lake. The lakes in the Alps are given as an example of a similar anthropogenic pollution scenario. The treatment of a Lake District tarn with bone meal is described. The article goes on to discuss the composition of plankton throughout the year under a variety of climatic conditions. A figure shows seasonal variation in the consistuents of phytoplankton in Windermere (north basin)

Meeting them Half way: My Life as a Teacher, Tutor, Consultant

By the time I arrived at the University of Texas Undergraduate Writing Center, I had already worked on writing with adult education students–at a Brooklyn community center–and with undergraduates at the State University of New York at Albany. My titles had been teacher and tutor, respectively. Then it became consultant at UT, and I began to think about the tone the title gives to everyone’s expectations–my own, as well as the students'.University Writing Cente