Distinguished orbits and the L–S category of simply connected compact Lie groups

We show that the Lusternik–Schnirelmann category of a simple, simply connected, compact Lie group G is bounded above by the sum of the relative categories of certain distinguished conjugacy classes in G corresponding to the vertices of the fundamental alcove for the action of the affine Weyl group o...

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Bibliographic Details
Published inTopology and its applications Vol. 156; no. 15; pp. 2443 - 2451
Main Authors Hunziker, Markus, Sepanski, Mark R.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2009
Subjects
Compact Lie groups
Conjugacy classes
L–S category
L–S category
Conjugacy classes
Compact Lie groups
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Summary:We show that the Lusternik–Schnirelmann category of a simple, simply connected, compact Lie group G is bounded above by the sum of the relative categories of certain distinguished conjugacy classes in G corresponding to the vertices of the fundamental alcove for the action of the affine Weyl group on the Lie algebra of a maximal torus of G.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2009.06.009