Chris Kottke, New College of Florida
"Compactification of monopole moduli spaces and Sen's conjecture"
The moduli spaces, M_k, of nonabelian magnetic monopoles of charge k form a well-known family of noncompact hyperKahler manifolds. Though there are partial results by Segal, Selby, and Hitchin, Sen's 1994 conjecture concerning the dimensions of the L^2 cohomology spaces (i.e., the spaces of square-integrable harmonic forms) of the M_k remains open. As a step toward finishing the proof of this conjecture, we construct compactifications of the M_k as manifolds with corners, on which the hyperKahler metrics are well-behaved. This will allow the application of new geometric microlocal techniques to the study of harmonic forms. This is joint work with K. Fritzcsh, R. Melrose, and M. Singer.
MC 5413