Analysis of S 2-valued maps and Faddeev's model

Dave Auckly, Lev Kapitanski

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


In this paper we consider a generalization of the Faddeev model for the maps from a closed three-manifold into the two-sphere. We give a novel representation of smooth S 2-valued maps based on flat connections. This representation allows us to obtain an analytic description of the homotopy classes of S 2-valued maps that generalizes to Sobolev maps. It also leads to a new proof of an old theorem of Pontrjagin. For the generalized Faddeev model, we prove the existence of minimizers in every homotopy class.

Original languageEnglish (US)
Pages (from-to)611-620
Number of pages10
JournalCommunications in Mathematical Physics
Issue number3
StatePublished - Jun 1 2005

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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