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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Copolarity of isometric actions


Authors: Claudio Gorodski, Carlos Olmos and Ruy Tojeiro
Journal: Trans. Amer. Math. Soc. 356 (2004), 1585-1608
MSC (2000): Primary 57S15; Secondary 53C20
Published electronically: September 22, 2003
MathSciNet review: 2034320
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Abstract: We introduce a new integral invariant for isometric actions of compact Lie groups, the copolarity. Roughly speaking, it measures how far from being polar the action is. We generalize some results about polar actions in this context. In particular, we develop some of the structural theory of copolarity $k$ representations, we classify the irreducible representations of copolarity one, and we relate the copolarity of an isometric action to the concept of variational completeness in the sense of Bott and Samelson.


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Additional Information

Claudio Gorodski
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, São Paulo, SP 05508-090, Brazil
Email: gorodski@ime.usp.br

Carlos Olmos
Affiliation: Facultad de Matemática, Astronomía y Física, Universidad Nacional Córdoba, Medina Allende y Haya de la Torre, Ciudad Universitaria, 5000 Córdoba, Argentina
Email: olmos@mate.uncor.edu

Ruy Tojeiro
Affiliation: Departamento de Matemática, Universidade Federal de São Carlos, Rodovia Washington Luiz, Km 235, São Carlos, SP 13565-905, Brazil
Email: tojeiro@dm.ufscar.br

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03427-5
PII: S 0002-9947(03)03427-5
Received by editor(s): October 17, 2002
Received by editor(s) in revised form: March 3, 2003
Published electronically: September 22, 2003
Additional Notes: The first author was supported in part by CNPq grant 300720/93-9 and by FAPESP grant 01/04793-8.
The second author was supported by Universidad Nacional de Córdoba and CONICET, and supported in part by CIEM, Secyt-UNC and ANPCYT
The third author was supported in part by CNPq grant 300229/92-5 and FAPESP grant 01/05318-1.
Article copyright: © Copyright 2003 American Mathematical Society