The topological period-index problem over 6-complexes

By comparing the Postnikov towers of the classifying spaces of projective unitary groups and the differentials in a twisted Atiyah-Hirzebruch spectral sequence, we deduce a lower bound on the topological index in terms of the period, and solve the topological version of the period-index problem in full for finite CW complexes of dimension at most 6. Conditions are established that, if they were met in the cohomology of a smooth complex 3-fold variety, would disprove the ordinary period-index conjecture. Examples of higher-dimensional varieties meeting these conditions are provided. We use our results to furnish an obstruction to realizing a period-2 Brauer class as the class associated to a sheaf of Clifford algebras, and varieties are constructed for which the total Clifford invariant map is not surjective. No such examples were previously known.Comment: To appear in J. To

Detection of H-alpha emission from the Magellanic Stream: evidence for an extended gaseous Galactic halo

We have detected faint, diffuse H$\alpha emission from several points along the Magellanic Stream, using the Rutgers Fabry--Perot Interferometer at the CTIO 1.5-m telescope. At points on the leading edges of the H I clouds MS II, MS III, and MS IV, we detect H$\alpha emission of surface brightness $0.37 \pm 0.02$ Rayleighs, $0.21 \pm 0.04$ R, and $0.20 \pm 0.02$ R respectively, corresponding to emission measures of 1.0 to 0.5 \cmsixpc. We have observed several positions near the MS IV concentration, and find that the strongest emission is on the sharp leading-edge density gradient. There is less emission at points away from the gradient, and halfway between MS III and MS IV the H$\alpha surface brightness is$< 0.04$R. We attribute the H$\alpha emission at cloud leading edges to heating of the Stream clouds by ram pressure from ionized gas in the halo of the Galaxy. These observations suggest that ram pressure from halo gas plays a large role in stripping the Stream out of the Magellanic Clouds. They also suggest the presence of a relatively large density of gas, $n_{\rm H} \sim 10^{-4} cm^{-3}$, in the Galactic halo at $\sim 50$ kpc radius, and far above the Galactic plane, $b \sim -80\deg$. This implies that the Galaxy has a very large baryonic, gaseous extent, and supports models of Lyman-$\alpha and metal-line QSO absorption lines in which the absorption systems reside in extended galactic halos.Comment: 15 pages, aaspp latex, + 1 table & 3 figures. Accepted in A.J. Also available from http://www.physics.rutgers.edu/~bweiner/astro/papers