Holomorphic curves in loop groups

Martin Guest, A. N. Pressley

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

It was observed by Atiyah that there is a correspondence between based gauge equivalence classes of SUn-instantons over S4 of charge d on the one hand, and based holomorphic curves of genus zero in ΩSUn of degree d on the other hand. In this paper we study the parameter space of such holomorphic curves which have the additional property that they lie entirely in the subgroup ΩalgSUn of algebraic loops. We describe a cell decomposition of this parameter space, and compute its complex dimension to be (2 n-1)d.

Original languageEnglish
Pages (from-to)511-527
Number of pages17
JournalCommunications in Mathematical Physics
Volume118
Issue number3
DOIs
Publication statusPublished - 1988 Sep
Externally publishedYes

Fingerprint

Holomorphic Curve
Loop Groups
Parameter Space
Cell Decomposition
Michael Francis Atiyah
Instantons
curves
subgroups
instantons
Equivalence class
equivalence
Gauge
Genus
Correspondence
Charge
Subgroup
decomposition
Zero
cells

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

Holomorphic curves in loop groups. / Guest, Martin; Pressley, A. N.

In: Communications in Mathematical Physics, Vol. 118, No. 3, 09.1988, p. 511-527.

Research output: Contribution to journalArticle

Guest, Martin ; Pressley, A. N. / Holomorphic curves in loop groups. In: Communications in Mathematical Physics. 1988 ; Vol. 118, No. 3. pp. 511-527.
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