2004/03/14 by Dave Auckly, Auckly, Dave, Lev Kapitanski +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Topological and Geometric Data Analysis #math-ph #math.GT #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0403025
arxiv created 2004/03/14 · openalex publication_date 2004/03/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 S2-valued maps based on flat connections. This representation allows us to obtain an analytic description of the homotopy classes of S2-valued maps that generalizes to Sobolev maps. It also leads to a new proof an old theorem of Pontrjagin. For the generalized Faddeev model, we prove the existence of minimizers in every homotopy class.