A bicategory of reduced orbifolds from the point of view of differential geometry

JOURNAL OF GEOMETRY AND PHYSICS

卷:108

Article

Tommasini, Matteo¹ 

[1] Univ Luxembourg, L-1359 Luxembourg, Luxembourg

关键词: Reduced orbifolds;    Lie groupoids;    Differentiable stacks;    2-categories;    Bicategories;   

DOI  :  10.1016/j.geomphys.2016.03.025

来源: Elsevier

【 摘 要 】

We describe a bicategory (Red orb) of reduced orbifolds in the framework of classical differential geometry (i.e. without any explicit reference to the notions of Lie groupoids or differentiable stacks, but only using orbifold atlases, local lifts and changes of charts). In order to construct such a bicategory, we firstly define a 2-category (Red At1) whose objects are reduced orbifold atlases (on any paracompact, second countable, Hausdorff topological space). The definition of morphisms is obtained as a slight modification of a definition by A. Pohl, while the definitions of 2-morphisms and compositions of them are new in this setup. Using the bicalculus of fractions described by D. Pronk, we are able to construct the bicategory (Red Orb) from the 2-category (Red At1). We prove that (Red Orb) is equivalent to the bicategory of reduced orbifolds described in terms of proper, effective, etale Lie groupoids by D. Pronk and I. Moerdijk and to the well-known 2-category of reduced orbifolds constructed from a suitable class of differentiable Deligne-Mumford stacks. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free