Journal of the Mathematical Society of Japan

The category of reduced orbifolds in local charts

Anke D. POHL

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Abstract

It is well-known that reduced smooth orbifolds and proper effective foliation Lie groupoids form equivalent categories. However, for certain recent lines of research, equivalence of categories is not sufficient. We propose a notion of maps between reduced smooth orbifolds and a definition of a category in terms of marked proper effective étale Lie groupoids such that the arising category of orbifolds is isomorphic (not only equivalent) to this groupoid category.

Article information

Source
J. Math. Soc. Japan Volume 69, Number 2 (2017), 755-800.

Dates
First available in Project Euclid: 20 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1492653646

Digital Object Identifier
doi:10.2969/jmsj/06920755

Subjects
Primary: 57R18: Topology and geometry of orbifolds 22A22: Topological groupoids (including differentiable and Lie groupoids) [See also 58H05]
Secondary: 58H05: Pseudogroups and differentiable groupoids [See also 22A22, 22E65]

Keywords
reduced orbifolds orbifold maps groupoids groupoid homomorphisms

Citation

POHL, Anke D. The category of reduced orbifolds in local charts. J. Math. Soc. Japan 69 (2017), no. 2, 755--800. doi:10.2969/jmsj/06920755. https://projecteuclid.org/euclid.jmsj/1492653646


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