Geometry and analysis in nonlinear sigma models
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D. Auckly, L. Kapitanski and J. M. Speight
Translated by: the authors - St. Petersburg Math. J. 18 (2007), 1-19
- DOI: https://doi.org/10.1090/S1061-0022-06-00940-X
- Published electronically: November 27, 2006
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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.References
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Bibliographic Information
- D. Auckly
- Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
- MR Author ID: 305151
- L. Kapitanski
- Affiliation: Department of Mathematics, University of Miami, Coral Gabels, Florida 33124
- MR Author ID: 191377
- J. M. Speight
- Affiliation: School of Mathematics, University of Leeds, Leeds LS2 9JT, England
- Received by editor(s): June 16, 2005
- Published electronically: November 27, 2006
- Additional Notes: The first author was partially supported by NSF grant DMS-0204651. The second author was partially supported by NSF grant DMS-0436403. The third author was partially supported by EPSRC grant GR/R66982/01.
- © Copyright 2006 American Mathematical Society
- Journal: St. Petersburg Math. J. 18 (2007), 1-19
- MSC (2000): Primary 81T13
- DOI: https://doi.org/10.1090/S1061-0022-06-00940-X