Quotients of singular foliations and Lie 2-group actions
- Androulidakis-Skandalis (2009) showed that every singular foliation has an associated topological groupoid, called holonomy groupoid. In this note, we exhibit some functorial properties of this assignment: if a foliated manifold (M, FM ) is the quotient of a foliated manifold (P, FP ) along a surjective submersion with connected fibers, then the same is true for the corresponding holonomy groupoids. For quotients by a Lie group action, an analogue statement holds under suitable assumptions, yielding a Lie 2-group action on the holonomy groupoid.
| Author details: | Alfonso GarmendiaORCiD, Marco Zambon |
|---|---|
| DOI: | https://doi.org/10.4171/JNCG/434 |
| ISSN: | 1661-6952 |
| ISSN: | 1661-6960 |
| Title of parent work (English): | Journal of noncommutative geometry |
| Publisher: | EMS Press, an imprint of the European Mathematical Society - EMS - Publishing House GmbH, Institut für Mathematik, Technische Universität Berlin |
| Place of publishing: | Berlin |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2021 |
| Publication year: | 2021 |
| Release date: | 2023/11/10 |
| Tag: | Lie groupoid; fibration; singular foliation |
| Volume: | 15 |
| Issue: | 4 |
| Number of pages: | 33 |
| First page: | 1251 |
| Last Page: | 1283 |
| Funding institution: | long term structural funding - Methusalem grant of the Flemish Government; FWO under EOS project [G0H4518N]; FWO research project (Belgium)FWO [G083118N] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Gold Open-Access |
| DOAJ gelistet | |
| License (German): |  CC-BY - Namensnennung 4.0 International |
