K-theory of noncommutative Bieberbach manifolds

We compute $K-theory of noncommutative Bieberbach manifolds, which quotients of a three-dimensional noncommutative torus by a free action of a cyclic group Z_N, N=2,3,4,6.Comment: 19 page

Cosmic microwave background anisotropies in multi-connected flat spaces

This article investigates the signature of the seventeen multi-connected flat spaces in cosmic microwave background (CMB) maps. For each such space it recalls a fundamental domain and a set of generating matrices, and then goes on to find an orthonormal basis for the set of eigenmodes of the Laplace operator on that space. The basis eigenmodes are expressed as linear combinations of eigenmodes of the simply connected Euclidean space. A preceding work, which provides a general method for implementing multi-connected topologies in standard CMB codes, is then applied to simulate CMB maps and angular power spectra for each space. Unlike in the 3-torus, the results in most multi-connected flat spaces depend on the location of the observer. This effect is discussed in detail. In particular, it is shown that the correlated circles on a CMB map are generically not back-to-back, so that negative search of back-to-back circles in the WMAP data does not exclude a vast majority of flat or nearly flat topologies.Comment: 33 pages, 19 figures, 1 table. Submitted to PR

Atmospheric Chemical Transport Based on High Resolution Model- Derived Winds: A Case Study

Flight 10 of NASA's Subsonic Assessment (SASS) Ozone and Nitrogen Oxide Experiment (SONEX) extended southwest of Lajes, Azores. A variety of chemical signatures were encountered. These signatures are examined in detail, relating them to meteorological data from a high resolution numerical model having horizontal grid spacing of 30 and 90 km and 26 vertical levels. The meteorological output at hourly intervals is used to create backward trajectories from the locations of the chemical signatures. Four major categories of chemical signatures are discussed-stratospheric, lightning, continental pollution, and a transition layer. The strong stratospheric signal is encountered just south of the Azores in a region of depressed tropopause height. Three chemical signatures at different altitudes in the upper troposphere are attributed to lightning. Backward trajectories arriving at locations of these signatures are related to locations of cloud-to-ground lightning. Results show that the trajectories pass through regions of lightning 1-2 days earlier over the eastern Gulf of Mexico and off the southeast coast of the United States. The lowest leg of the flight exhibits a chemical signature consistent with continental pollution. Trajectories arriving at this signature are found to pass over the highly populated Northeast Corridor of the United States. Surface based pollution apparently is lofted to the altitudes of the trajectories by convective clouds along the East Coast that did not contain lightning. Finally, a chemical transition layer is described. Its chemical signature is intermediate to those of lightning and continental pollution. Trajectories arriving in this layer pass between the trajectories of the lightning and pollution signatures. Thus, they probably are impacted by both sources

Combinatorial 3-manifolds with transitive cyclic symmetry

In this article we give combinatorial criteria to decide whether a transitive cyclic combinatorial d-manifold can be generalized to an infinite family of such complexes, together with an explicit construction in the case that such a family exists. In addition, we substantially extend the classification of combinatorial 3-manifolds with transitive cyclic symmetry up to 22 vertices. Finally, a combination of these results is used to describe new infinite families of transitive cyclic combinatorial manifolds and in particular a family of neighborly combinatorial lens spaces of infinitely many distinct topological types.Comment: 24 pages, 5 figures. Journal-ref: Discrete and Computational Geometry, 51(2):394-426, 201