Gluing an infinite number of instantons

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Abstract

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 ASD connections have infinite energy in general. Moreover they have an infinite dimensional parameter space. Our construction is a generalization of Donaldson's "alternating method".

Original languageEnglish
Pages (from-to)107-131
Number of pages25
JournalNagoya Mathematical Journal
Volume188
Publication statusPublished - Dec 1 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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