Toric Genera

Our primary aim is to develop a theory of equivariant genera for stably complex manifolds equipped with compatible actions of a torus T^k. In the case of omnioriented quasitoric manifolds, we present computations that depend only on their defining combinatorial data; these draw inspiration from analogous calculations in toric geometry, which seek to express arithmetic, elliptic, and associated genera of toric varieties in terms only of their fans. Our theory focuses on the universal toric genus \Phi, which was introduced independently by Krichever and Loeffler in 1974, albeit from radically different viewpoints. In fact \Phi is a version of tom Dieck's bundling transformation of 1970, defined on T^k-equivariant complex cobordism classes and taking values in the complex cobordism algebra of the classifying space. We proceed by combining the analytic, the formal group theoretic, and the homotopical approaches to genera, and refer to the index theoretic approach as a recurring source of insight and motivation. The resultant flexibility allows us to identify several distinct genera within our framework, and to introduce parametrised versions that apply to bundles equipped with a stably complex structure on the tangents along their fibres. In the presence of isolated fixed points, we obtain universal localisation formulae, whose applications include the identification of Krichever's generalised elliptic genus as universal amongst genera that are rigid on SU-manifolds. We follow the traditions of toric geometry by working with a variety of illustrative examples wherever possible. For background and prerequisites we attempt to reconcile the literature of east and west, which developed independently for several decades after the 1960s.Comment: 35 pages, LaTeX. In v2 references made to the index theoretical approach to genera; rigidity and multiplicativity results improved; acknowledgements adde

Nonunion Employee Representation in North America: Diversity, Controversy, and Uncertain Future

The diverse conceptual perspectives and practical experiences with nonunion employee representation (NER) in the United States and Canada are reviewed. We first propose a 6 dimensional descriptive schema to categorize observed NER practices. Dimensions of diversity include (1) form, (2) function, (3) subjects, (4) representation characteristics, (5) extent of power, and (6) degree of permanence. We then turn to the NER controversy, which is a tangled skein consisting of many different threads of values and prescriptions. To unbundle the controversy, we develop four "faces" of NER - (1) evolutionary voice, (2) unity of interest; (3) union avoidance, and (4) complementary voice -- so that future research can more consciously test the validity of competing perspectives with hard data. Generalizing about NER is problematic because of these many dimensions of diversity, and because NER is viewed through different ideological and conceptual lenses. We conclude that NER's future trajectory is uncertain due to conflicting trends but in the short-run is most likely to remain a modest-sized phenomenon. Working Paper 06-4

Effect of spin on electron motion in a random magnetic field

We consider properties of a two-dimensional electron system in a random magnetic field. It is assumed that the magnetic field not only influences orbital electron motion but also acts on the electron spin. For calculations, we suggest a new trick replacing the initial Hamiltonian by a Dirac Hamiltonian. This allows us to do easily a perturbation theory and derive a supermatrix sigma model, which takes a form of the conventional sigma model with the unitary symmetry. Using this sigma model we calculate several correlation functions including a spin-spin correlation function. As compared to the model without spin, we get different expressions for the single-particle lifetime and the transport time. The diffusion constant turns out to be 2 times smaller than the one for spinless particles.Comment: 7 pages, revtex, result of the spin correlation function corrected, Appendix adde