The conjugacy problem for automorphism groups of countable homogeneous structures

We consider the conjugacy problem for the automorphism groups of a number of countable homogeneous structures. In each case we find the precise complexity of the conjugacy relation in the sense of Borel reducibility

Pion-Nucleon Scattering at Low Energies

We study pion-nucleon scattering at tree level with a chiral lagrangian of pions, nucleons, and $\Delta$-isobars using a K-matrix unitarization procedure. Evaluating the scattering amplitude to order $Q^2$, where $Q$ is a generic small momentum scale, we obtain a good fit to the experimental phase shifts for pion center-of-mass kinetic energies up to $50$MeV. The fit can be extended to 150 MeV when we include the order-$Q^3$ contributions. Our results are independent of the off-shell $\Delta$ parameter.Comment: 13 pages, RevTex, Two tables and two figures, Minor changes, To appear in PR

A global conformal extension theorem for perfect fluid Bianchi space-times

A global extension theorem is established for isotropic singularities in polytropic perfect fluid Bianchi space-times. When an extension is possible, the limiting behaviour of the physical space-time near the singularity is analysed.Comment: 13 pages, no figures, revised and shortened, improved proof of main theorem, some correction

A Faint Star-Forming System Viewed Through the Lensing Cluster Abell 2218: First Light at z~5.6?

We discuss the physical nature of a remarkably faint pair of Lyman alpha-emitting images discovered close to the giant cD galaxy in the lensing cluster Abell 2218 (z=0.18) during a systematic survey for highly-magnified star-forming galaxies beyond z=5. A well-constrained mass model suggests the pair arises via a gravitationally-lensed source viewed at high magnification. Keck spectroscopy confirms the lensing hypothesis and implies the unlensed source is a very faint (I~30) compact (<150 pc) and isolated object at z=5.576 whose optical emission is substantially contained within the Lyman alpha emission line; no stellar continuum is detectable. The available data suggest the source is a promising candidate for an isolated ~10^6 solar mass system seen producing its first generation of stars close to the epoch of reionization.Comment: 11 pages, 3 figures, to appear in Ap J Lett, minor revision following referee's repor