Gluing an infinite number of instantons

Details Gluing an infinite number of instantons Gluing an infinite number of instantons

2005-08-01

arxiv.org/abs/math/0508049v4

Nagoya Mathematical Journal, Vol. 188 (2007), 107-131

Mathematics

Differential Geometry

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Scientific paper

This paper is one step toward infinite energy gauge theory and the geometry of infinite dimensional moduli spaces. We generalize a gluing construction in the usual Yang-Mills gauge theory to an ``infinite energy'' situation. We show that we can glue an infinite number of instantons, and that the resulting instantons have infinite energy in general. Moreover we show that they have an infinite dimensional parameter space. Our construction is a generalization of Donaldson's ``alternating method''.

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