极作用的等变LS-范畴
The Equivariant LS-Category of Polar Actions
摘要：
我们将给出任意真作用量的等变Lusternik-Schnirelmann范畴在轨道类型分层意义下的一个下界，以及真极作用量的等变Lusternik-Schnirelmann范畴在广义外尔群意义下的一个上界.作为应用，我们重新证明了Singhof的一个定理，该定理决定了U（n）和SU（n）的经典Lusternik-Schnirelmann范畴.
英文摘要：
We will provide a lower bound for the equivariant Lusternik-Schnirelmann category of an arbitrary proper action in terms of the stratification by orbit types, and an upper bound for proper polar actions in terms of the equivariant Lusternik-Schnirelmann category of its generalized Weyl group. As an application we reprove a theorem of Singhof that determines the classical Lusternik-Schnirelmann category for U(n) and SU(n).
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