Holomorphic curves in loop groups

M. A. Guest, A. N. Pressley

Research output: Contribution to journalArticle

5 Citations (Scopus)


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
Issue number3
Publication statusPublished - 1988 Sep 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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