2002/08/13 by Cláudio Gorodski, Claudio Gorodski, Carlos Olmos +4 · 1 citation
Mathematics · #57S15 (Primary) 53C20 (Secondary) #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:53C20 #msc:57S15
paper · pdf · doi:10.48550/arxiv.math/0208105
23 pages, Latex; September17th, 2002: added section 5 and final question 2, added references, and changed subsection 3.3; October 3rd, 2002: new introduction, changes in corollary 5.3 and final question 2
openalex publication_date 2002/08/13 · arxiv created 2002/10/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.