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Algebra i Analiz, 2006, Volume 18, Issue 1, Pages 3–33 (Mi aa58)  

This article is cited in 5 scientific papers (total in 5 papers)

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Geometry and analysis in nonlinear sigma models

D. Aucklya, L. Kapitanskib, J. M. Speightc

a Department of Mathematics, Kansas State University, Manhattan, Kansas USA
b Department of Mathematics, University of Miami, Coral Gabels, Florida, USA
c Department of Pure Mathematics, University of Leeds, Leeds, England

Abstract: The configuration space of a nonlinear sigma model is the space of maps from one manifold to another. This paper reviews the authors' work on nonlinear sigma models with target a homogeneous space. It begins with a description of the components, fundamental group, and cohomology of such configuration spaces, together with the physical interpretations of these results. The topological arguments given generalize to Sobolev maps. The advantages of representing homogeneous-space-valued maps by flat connections are described, with applications to the homotopy theory of Sobolev maps, and minimization problems for the Skyrme and Faddeev functionals. The paper concludes with some speculation about the possibility of using these techniques to define new invariants of manifolds.

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English version:
St. Petersburg Mathematical Journal, 2007, 18:1, 1–19

Bibliographic databases:

MSC: 81T13
Received: 16.06.2005

Citation: D. Auckly, L. Kapitanski, J. M. Speight, “Geometry and analysis in nonlinear sigma models”, Algebra i Analiz, 18:1 (2006), 3–33; St. Petersburg Math. J., 18:1 (2007), 1–19

Citation in format AMSBIB
\Bibitem{AucKapSpe06}
\by D.~Auckly, L.~Kapitanski, J.~M.~Speight
\paper Geometry and analysis in nonlinear sigma models
\jour Algebra i Analiz
\yr 2006
\vol 18
\issue 1
\pages 3--33
\mathnet{http://mi.mathnet.ru/aa58}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2225211}
\zmath{https://zbmath.org/?q=an:1118.58008}
\elib{http://elibrary.ru/item.asp?id=9212597}
\transl
\jour St. Petersburg Math. J.
\yr 2007
\vol 18
\issue 1
\pages 1--19
\crossref{https://doi.org/10.1090/S1061-0022-06-00940-X}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kholodenko A.L., “Veneziano amplitudes, spin chains, and string models”, Int. J. Geom. Methods Mod. Phys., 6:5 (2009), 769–803  crossref  mathscinet  zmath  isi  scopus
    2. Kholodenko A., “Veneziano amplitudes, spin chains and Abelian reduction of QCD”, J. Geom. Phys., 59:5 (2009), 600–619  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Liu Luofei, “Homotopy counting $S^1$- and $S^2$-valued maps with prescribed dilatation”, Bull. Lond. Math. Soc., 41 (2009), 124–136  crossref  mathscinet  zmath  isi  scopus
    4. Auckly D., Kapitanski L., “The Pontrjagin–Hopf invariants for Sobolev maps”, Commun. Contemp. Math., 12:1 (2010), 121–181  crossref  mathscinet  zmath  isi  elib  scopus
    5. Kapitanski L., “Analytic Form of the Pontrjagin-Hopf Invariants”, Complex Analysis and Dynamical Systems IV, Pt 2: General Relativity, Geometry, and Pde, Contemporary Mathematics, 554, eds. Agranovsky M., BenArtzi M., Galloway G., Karp L., Reich S., Shoikhet D., Weinstein G., Zalcman L., Amer Mathematical Soc, 2011, 105–113  crossref  mathscinet  zmath  isi
  • Алгебра и анализ St. Petersburg Mathematical Journal
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