Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-08T11:31:16.070Z Has data issue: false hasContentIssue false
  • English
  • Français

Gluing an Infinite Number of Instantons

Published online by Cambridge University Press:  11 January 2016

Masaki Tsukamoto
Masaki Tsukamoto*
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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”.

Keywords

58D2753C0746T05
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 188 , December 2007 , pp. 107 - 131
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

References

[A] Angenent, S., The shadowing lemma for elliptic PDE, Dynamics of Infinite Dimensional Systems, NATO Adv. Sci. Inst. Ser. F Comput. Systems Sci., 37, Springer, Berlin, 1987, pp. 7–22.Google Scholar
[D1] Donaldson, S. K., An application of gauge theory to four dimensional topology, J. Differential Geometry, 18 (1983), 279–315.Google Scholar
[D2] Donaldson, S. K., Connections, cohomology and the intersection forms of 4-manifolds, J. Differential Geometry, 24 (1986), 275–341.Google Scholar
[DFK] Donaldson, S. K., Furuta, M. and Kotschick, D., Floer homology groups in Yang-Mills theory, Cambridge University Press, Cambridge, 2002.Google Scholar
[DK] Donaldson, S. K. and Kronheimer, P. B., The geometry of four-manifolds, Oxford University Press, New York, 1990.CrossRefGoogle Scholar
[FU] Freed, D. S. and Uhlenbeck, K. K., Instantons and four-manifolds, Second edition, Springer-Verlag, New York, 1991.Google Scholar
[MNR] Macrí, M., Nolasco, M. and Ricciardi, T., Asymptotics for selfdual vortices on the torus and on the plane: a gluing technique, SIAM J. Math. Anal., 37 (2005), 1–16.Google Scholar
[T1] Taubes, C. H., Self-dual Yang-Mills connections on non-self-dual 4-manifolds, J. Differential Geometry, 17 (1982), 139–170.Google Scholar
[T2] Taubes, C. H., Self-dual connections on 4-manifolds with indefinite intersection matrix, J. Differential Geometry, 19 (1984), 517–560.CrossRefGoogle Scholar