Abstract
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 language | English (US) |
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Pages (from-to) | 611-620 |
Number of pages | 10 |
Journal | Communications in Mathematical Physics |
Volume | 256 |
Issue number | 3 |
DOIs | |
State | Published - Jun 1 2005 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics