1210.3275 (Chris Kottke)

Callias' index theorem and monopole deformation    [PDF]

Chris Kottke

A generalization of Callias' index theorem for self adjoint Dirac operators with skew adjoint potentials on asymptotically conic manifolds is presented in which the potential term may have constant rank nullspace at infinity. This is subsequently used to compute the formal dimension of the space of SU(2) magnetic monopoles on asymptotically conic 3-manifolds. The dimension is shown to agree with the one computed by Braam for monopoles on certain asymptotically hyperbolic manifolds.

View original: http://arxiv.org/abs/1210.3275