Provides the first counterexamples showing algebraic singular functions are not always dense in the ideal of C*-singular functions for certain étale non-Hausdorff groupoids, including a bundle of groups and one from a self-similar action.
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Constructs equivariant E-theory and a natural Baum-Connes assembly map for Fell bundles of inverse semigroups, covering maximal, reduced, and essential cases with applications to groupoids and Cartan pairs.
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Algebraic singular functions are not always dense in the ideal of $C^*$-singular functions
Provides the first counterexamples showing algebraic singular functions are not always dense in the ideal of C*-singular functions for certain étale non-Hausdorff groupoids, including a bundle of groups and one from a self-similar action.
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A Baum-Connes assembly map for essential semigroup crossed products
Constructs equivariant E-theory and a natural Baum-Connes assembly map for Fell bundles of inverse semigroups, covering maximal, reduced, and essential cases with applications to groupoids and Cartan pairs.