Introduces discretisation showing independent ample groupoids are equivalent to discrete ones and provides a method to build independent resolutions for computing homology and K-theory.
arXiv: 2409.02359
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
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UNVERDICTED 5representative citing papers
An ample groupoid is AF if and only if it has homological dimension zero.
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.
The relative Cuntz-Pimsner algebra of a groupoid correspondence is the groupoid C*-algebra of a new groupoid with an explicit description and universal property for actions on topological spaces.
Formulas are supplied for the type semigroup of C*-algebras arising from self-similar group actions on row-finite source-free graphs and from finite bipartite separated graphs.
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Discretisation and independent resolutions of ample groupoids
Introduces discretisation showing independent ample groupoids are equivalent to discrete ones and provides a method to build independent resolutions for computing homology and K-theory.
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A homological characterization of AF groupoids
An ample groupoid is AF if and only if it has homological dimension zero.
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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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Groupoid models for relative Cuntz-Pimsner algebras of groupoid correspondences
The relative Cuntz-Pimsner algebra of a groupoid correspondence is the groupoid C*-algebra of a new groupoid with an explicit description and universal property for actions on topological spaces.
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An introduction to separated graphs and their type semigroups
Formulas are supplied for the type semigroup of C*-algebras arising from self-similar group actions on row-finite source-free graphs and from finite bipartite separated graphs.