### 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 language | English |
---|---|

Pages (from-to) | 107-131 |

Number of pages | 25 |

Journal | Nagoya Mathematical Journal |

Volume | 188 |

Publication status | Published - Dec 1 2007 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Nagoya Mathematical Journal*,

*188*, 107-131.

**Gluing an infinite number of instantons.** / Tsukamoto, Masaki.

Research output: Contribution to journal › Article

*Nagoya Mathematical Journal*, vol. 188, pp. 107-131.

}

TY - JOUR

T1 - Gluing an infinite number of instantons

AU - Tsukamoto, Masaki

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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".

AB - 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".

UR - http://www.scopus.com/inward/record.url?scp=38349117201&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38349117201&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:38349117201

VL - 188

SP - 107

EP - 131

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

SN - 0027-7630

ER -