Categorical models for equivariant classifying spaces

Starting categorically, we give simple and precise models of equivariant classifying spaces. We need these models for work in progress in equivariant infinite loop space theory and equivariant algebraic K-theory, but the models are of independent interest in equivariant bundle theory and especially equivariant covering space theory.Comment: 29 pages. Revised version, to appear in AGT. Considerable changes of notation and organization and other changes aimed at making the paper more user friendl

Twisted equivariant K-theory of compact Lie group actions with maximal rank isotropy

We consider twisted equivariant K--theory for actions of a compact Lie group $G$ on a space $X$ where all the isotropy subgroups are connected and of maximal rank. We show that the associated rational spectral sequence \`a la Segal has a simple $E_2$--term expressible as invariants under the Weyl group of $G$. Namely, if $T$ is a maximal torus of $G$, they are invariants of the $\pi_1(X^T)$-equivariant Bredon cohomology of the universal cover of $X^T$ with suitable coefficients. In the case of the inertia stack $\Lambda Y$ this term can be expressed using the cohomology of $Y^T$ and algebraic invariants associated to the Lie group and the twisting. A number of calculations are provided. In particular, we recover the rational Verlinde algebra when $Y=\{*\}$.Comment: To appear in Journal of Mathematical Physics. Some mistakes have been corrected in Section

The refined transfer, bundle structures and algebraic K-theory

We give new homotopy theoretic criteria for deciding when a fibration with homotopy finite fibers admits a reduction to a fiber bundle with compact topological manifold fibers. The criteria lead to a new and unexpected result about homeomorphism groups of manifolds. A tool used in the proof is a surjective splitting of the assembly map for Waldhausen's functor A(X). We also give concrete examples of fibrations having a reduction to a fiber bundle with compact topological manifold fibers but which fail to admit a compact fiber smoothing. The examples are detected by algebraic K-theory invariants. We consider a refinement of the Becker-Gottlieb transfer. We show that a version of the axioms described by Becker and Schultz uniquely determines the refined transfer for the class of fibrations admitting a reduction to a fiber bundle with compact topological manifold fibers. In an appendix, we sketch a theory of characteristic classes for fibrations. The classes are primary obstructions to finding a compact fiber smoothing.Comment: This version contains mostly minor revision

Rigid string instantons are pseudo-holomorphic curves

We show how to find explicit expressions for rigid string instantons for general 4-manifold $M$. It appears that they are pseudo-holomorphic curves in the twistor space of $M$. We present explicit formulae for $M=R^4, S^4$. We discuss their properties and speculate on relations to topology of 4-manifolds and the theory of Yang-Mills fields.Comment: 18 pages,Late

Classification of Invariant Star Products up to Equivariant Morita Equivalence on Symplectic Manifolds

In this paper we investigate equivariant Morita theory for algebras with momentum maps and compute the equivariant Picard groupoid in terms of the Picard groupoid explicitly. We consider three types of Morita theory: ring-theoretic equivalence, *-equivalence and strong equivalence. Then we apply these general considerations to star product algebras over symplectic manifolds with a Lie algebra symmetry. We obtain the full classification up to equivariant Morita equivalence.Comment: 28 pages. Minor update, fixed typos

Methane Flux from Drained Northern Peatlands: Effect of a Persistent Water Table Lowering on Flux

Measurements of CH4 flux from drained and undrained sites in three northern Ontario peatlands (a treed fen, a forested bog, and a treed bog) were made from the beginning of May to the end of October 1991. In the drained portions, the water table had been lowered between 0.1 and 0.5 m, compared to the water table of the undrained portion of the peatlands. The mean seasonal CH4 flux from the undrained portions of three peatlands was small, ranging from 0 to 8 mg m-2d-1, but similar to the CH4 flux from other treed and forested northern peatlands. The mean seasonal CH4 flux from the drained portion of the peatlands was either near zero or slightly negative (i.e., uptake): fluxes ranged from 0.1 to -0.4 mg m-2d-1. Profiles of CH4 in the air-filled pores in the unsaturated zone, and the water-filled pores of the saturated zone of the peat at the undrained sites, showed that all the CH4 produced at depth was consumed within 0.2 m of the water table and that atmospheric CH4 was consumed in the upper 0.15 m of the peatland. On the basis of laboratory incubations of peat slurries to determine CH4 production and consumption potentials, the lowering of the water table eliminated the near-surface zone of CH4 production that existed in the undrained peatland. However, drainage did not alter significantly the potential for CH4 oxidation between the water table and peatland surface but increased the thickness of the layer over which CH4 oxidation could take place. These changes occurred with a drop in the mean summer water table of only 0.1 m (from -0.2 to -0.3 m) suggesting that only a small negative change in soil moisture would be required to significantly reduce CH4 flux from northern peatlands

Invasive aspergillosis mimicking metastatic lung cancer

In a patient with a medical history of cancer, the most probable diagnosis of an (18)FDG-avid pulmonary mass combined with intracranial abnormalities on brain imaging is metastasized cancer. However, sometimes a differential diagnosis with an infectious cause such as aspergillosis can be very challenging as both cancer and infection are sometimes difficult to distinguish. Pulmonary aspergillosis can present as an infectious pseudotumour with clinical and imaging characteristics mimicking lung cancer. Even in the presence of cerebral lesions, radiological appearance of abscesses can look like brain metastasis. These similarities can cause significant diagnostic difficulties with a subsequent therapeutic delay and a potential adverse outcome. Awareness of this infectious disease that can mimic lung cancer, even in an immunocompetent patient, is important. We report a case of a 65-year-old woman with pulmonary aspergillosis disseminated to the brain mimicking metastatic lung cancer

Potential climatic transitions with profound impact on Europe

We discuss potential transitions of six climatic subsystems with large-scale impact on Europe, sometimes denoted as tipping elements. These are the ice sheets on Greenland and West Antarctica, the Atlantic thermohaline circulation, Arctic sea ice, Alpine glaciers and northern hemisphere stratospheric ozone. Each system is represented by co-authors actively publishing in the corresponding field. For each subsystem we summarize the mechanism of a potential transition in a warmer climate along with its impact on Europe and assess the likelihood for such a transition based on published scientific literature. As a summary, the ‘tipping’ potential for each system is provided as a function of global mean temperature increase which required some subjective interpretation of scientific facts by the authors and should be considered as a snapshot of our current understanding. <br/