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arXiv · 2010.16113

Filtering germs: Groupoids associated to inverse semigroups

Becky Armstrong·Lisa Orloff Clark·Astrid an Huef·Malcolm Jones·Ying-Fen Lin
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Abstract

We investigate various groupoids associated to an arbitrary inverse semigroup with zero. We show that the groupoid of filters with respect to the natural partial order is isomorphic to the groupoid of germs arising from the standard action of the inverse semigroup on the space of idempotent filters. We also investigate the restriction of this isomorphism to the groupoid of tight filters and to the groupoid of ultrafilters.

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Becky Armstrong, Lisa Orloff Clark, Astrid an Huef, Malcolm Jones, Ying-Fen Lin. 2020-10-30. Filtering germs: Groupoids associated to inverse semigroups. https://doi.org/10.1016/j.exmath.2021.07.001

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