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Electronic Research Announcements

ISSN 1079-6762



Unitons and their moduli

Author: Christopher Kumar Anand
Journal: Electron. Res. Announc. Amer. Math. Soc. 2 (1996), 7-16
MSC (1991): Primary 58E20, 58D27, 58G37
Comment: Additional information about this paper
MathSciNet review: 1405964
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Abstract: We sketch the proof that unitons (harmonic spheres in $\operatorname {U}(N)$) correspond to holomorphic `uniton bundles', and that these admit monad representations analogous to Donaldson's representation of instanton bundles. We also give a closed-form expression for the unitons involving only matrix operations, a finite-gap result (two-unitons have energy $\ge 4$), computations of fundamental groups of energy $\le 4$ components, new methods of proving discreteness of the energy spectrum and of Wood's Rationality Conjecture, a discussion of the maps into complex Grassmannians and some open problems.

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Additional Information

Christopher Kumar Anand
Affiliation: Mathematics Research Centre, University of Warwick, Coventry CV4 7AL, UK

Keywords: Uniton, harmonic map, chiral field, sigma model
Received by editor(s): September 19, 1995
Additional Notes: Research supported by NSERC and FCAR scholarships.
Communicated by: Eugenio Calabi
Article copyright: © Copyright 1996 American Mathematical Society