For compact Lie group actions on metrizable spaces, equivariant A-category is invariant under Morita equivalence, yielding Morita-invariant equivariant LS-category and invariant topological complexity, and hence an orbifold topological complexity.
Higher equivariant and invariant topological complexity
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abstract
In this paper we introduce the concepts of higher equivariant and invariant topological complexity; and study their properties. Then we compare them with equivariant LS-category. We give lower and upper bounds for these new invariants. We compute some of these invariants for moment angle complexes.
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2019 1verdicts
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Morita Invariance of Equivariant Lusternik-Schnirelmann Category and Invariant Topological Complexity
For compact Lie group actions on metrizable spaces, equivariant A-category is invariant under Morita equivalence, yielding Morita-invariant equivariant LS-category and invariant topological complexity, and hence an orbifold topological complexity.