4,310 research outputs found
On the complete integrability of the discrete Nahm equations
The discrete Nahm equations, a system of matrix valued difference equations,
arose in the work of Braam and Austin on half-integral mass hyperbolic
monopoles.
We show that the discrete Nahm equations are completely integrable in a
natural sense: to any solution we can associate a spectral curve and a
holomorphic line-bundle over the spectral curve, such that the discrete-time DN
evolution corresponds to walking in the Jacobian of the spectral curve in a
straight line through the line-bundle with steps of a fixed size. Some of the
implications for hyperbolic monopoles are also discussed
Principal Bundles and the Dixmier Douady Class
A systematic consideration of the problem of the reduction and extension of
the structure group of a principal bundle is made and a variety of techniques
in each case are explored and related to one another. We apply these to the
study of the Dixmier-Douady class in various contexts including string
structures, U-res bundles and other examples motivated by considerations from
quantum field theory.Comment: 28 pages, latex, no figures, uses amsmath, amsthm, amsfonts. Revised
version - only change a lot of irritating typos remove
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