Nagoya Mathematical Journal

Gluing an infinite number of instantons

Masaki Tsukamoto

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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".

Article information

Source
Nagoya Math. J., Volume 188 (2007), 107-131.

Dates
First available in Project Euclid: 17 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1197908745

Mathematical Reviews number (MathSciNet)
MR2371770

Zentralblatt MATH identifier
1147.53023

Subjects
Primary: 58D27: Moduli problems for differential geometric structures
Secondary: 53C07: Special connections and metrics on vector bundles (Hermite-Einstein- Yang-Mills) [See also 32Q20] 46T05: Infinite-dimensional manifolds [See also 53Axx, 57N20, 58Bxx, 58Dxx]

Keywords
Yang-Mills gauge theory gluing ASD connections infinite energy infinite dimensional moduli space Donaldson's alternating method

Citation

Tsukamoto, Masaki. Gluing an infinite number of instantons. Nagoya Math. J. 188 (2007), 107--131. https://projecteuclid.org/euclid.nmj/1197908745


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References

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