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

Dave Auckly, Lev Kapitanski

Research output: Contribution to journalArticle

18 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)611-620
Number of pages10
JournalCommunications in Mathematical Physics
Volume256
Issue number3
DOIs
StatePublished - Jun 2005

Fingerprint

Homotopy
Flat Connection
Three-manifolds
Minimizer
Model
theorems
Closed
Generalise
Theorem
Class
Generalization

ASJC Scopus subject areas

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

Cite this

Analysis of S 2-valued maps and Faddeev's model. / Auckly, Dave; Kapitanski, Lev.

In: Communications in Mathematical Physics, Vol. 256, No. 3, 06.2005, p. 611-620.

Research output: Contribution to journalArticle

@article{e4edb42567f14df88b7b1c3701a08468,
title = "Analysis of S 2-valued maps and Faddeev's model",
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.",
author = "Dave Auckly and Lev Kapitanski",
year = "2005",
month = "6",
doi = "10.1007/s00220-005-1289-6",
language = "English (US)",
volume = "256",
pages = "611--620",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer New York",
number = "3",

}

TY - JOUR

T1 - Analysis of S 2-valued maps and Faddeev's model

AU - Auckly, Dave

AU - Kapitanski, Lev

PY - 2005/6

Y1 - 2005/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=18244389952&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18244389952&partnerID=8YFLogxK

U2 - 10.1007/s00220-005-1289-6

DO - 10.1007/s00220-005-1289-6

M3 - Article

VL - 256

SP - 611

EP - 620

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -