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TY - CHAP
TI - Metric of Monopole Spaces
A2 - ATIYAH, MICHAEL FRANCIS
A2 - HITCHIN, NIGEL
AB - In the previous chapter we saw that the parameter space of based*k*-monopoles is a manifold*M*_{k}of dimension 4*k*, and Donaldson’s theorem gives us a simple explicit model of this manifold. We shall now go on to introduce and investigate the natural Riemannian metric of*M*_{k}. This is given by the*L*^{2}-norm of the “zero-modes”, i.e. the solutions of the linearized equations, and the first thing is to show that this is finite, that is, that the zero-modes are square-integrable. Because of the non-compactness of R^{3}this is not trivial, and it requires analytical justification. Fortunately, Taubes [44] has

EP - 27
PB - Princeton University Press
PY - 1988
SN - null
SP - 21
T2 - The Geometry and Dynamics of Magnetic Monopoles
UR - http://www.jstor.org/stable/j.ctt7zv206.7
Y2 - 2020/11/29/
ER -