Topology of Quadric Bundles

This paper begins with a description of cohomological invariants of non-degenerate quadric bundles, in terms of the cohomology rings of the classifying spaces of the general orthogonal groups. Following this, the Main Theorem of the paper determines the behavior of these invariants under the Gysin boundary map, when a quadric bundle degenerates over a divisor.Comment: 41 pages, LaTeX. Final version to appear in International Journal of Mathematics. Main theorem is now proved for arbitrary coefficients, not just for Z/(2) as in the first versio

The Boden-Hu conjecture holds precisely up to rank eight

Consider moduli schemes of vector bundles over a smooth projective curve endowed with parabolic structures over a marked point. Boden and Hu observed that a slight variation of the weights leads to a desingularisation of the moduli scheme, and they conjectured that one can always obtain a small resolution this way. The present text proves this conjecture in some cases (including all bundles of rank up to eight) and gives counterexamples in all other cases (in particular in every rank beyond eight). The main tool is a generalisation of Ext-groups involving more than two quasiparabolic bundles.Comment: 17 page

Effects of orbital exposure on Halar during the LDEF mission

Thermomechanical Analysis (TMA), Differential Scanning Calorimetry (DSC), and Thermogravimetric Analysis (TGA) were performed on samples of Halar exposed on the LDEF Mission for 6 years in orbit and unexposed Halar control samples. Sections 10-100 microns thick were removed from the exposed surface down to a depth of 1,000 microns through the 3 mm thick samples. The TMA and DSC results, which arise from the entire slice and not just its surface, showed no differences between the LDEF and the control samples. TMA scans were run from ambient to 300 C; results were compared by a tabulation of the glass transition temperatures. DSC scans were run from ambient to 700 C; the enthalpy of melting was compared for the samples as a function of section depth with the sample. The TGA results, which arise from the surface of the sample initially, showed a sharp increase in the topmost 50 micron section (the exposed, discolored side) in the weight loss of 170 C in oxygen. This weight loss dropped to bulk values in the range of depth of 50-200 microns. The control sample showed only a slight increase in weight loss as the top surface was approached. The LDEF Halar sample appears to be mechanically undamaged, with a surface layer which oxidizes faster as a result of orbital exposure