Quasifold groupoids and diffeological quasifolds
Yael Karshon, David Miyamoto

TL;DR
This paper develops a categorical framework for quasifolds and their groupoids, showing an equivalence between effective quasifold groupoids and their diffeological orbit spaces, extending previous work.
Contribution
It introduces a bicategory of quasifold groupoids and proves an equivalence with diffeological quasifolds under certain conditions, extending earlier results.
Findings
Effective quasifold groupoids are categorically equivalent to their diffeological orbit spaces.
The bicategory of quasifold groupoids embeds into the bicategory of Lie groupoids.
The results extend previous work on the structure of quasifolds and their groupoids.
Abstract
Quasifolds are spaces that are locally modelled by quotients of by countable affine group actions. These spaces first appeared in Elisa Prato's generalization of the Delzant construction, and special cases include leaf spaces of irrational linear flows on the torus, and orbifolds. We consider the category of diffeological quasifolds, which embeds in the category of diffeological spaces, and the bicategory of quasifold groupoids, which embeds in the bicategory of Lie groupoids, bibundles, and bibundle morphisms. We prove that, restricting to those morphisms that are locally invertible, and to quasifold groupoids that are effective, the functor taking a quasifold groupoid to its diffeological orbit space is an equivalence of the underlying categories. These results complete and extend earlier work with Masrour Zoghi.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra
