Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/45286
Title: Orbispaces as differentiable stratified spaces
Authors: Crainic, Marius 
Mestre, João Nuno 
Issue Date: 2017
Publisher: Springer Netherlands
Project: info:eu-repo/grantAgreement/FCT/5876/147205/PT 
Serial title, monograph or event: Letters in Mathematical Physics
Abstract: We present some features of the smooth structure and of the canonical stratification on the orbit space of a proper Lie groupoid. One of the main features is that of Morita invariance of these structures—it allows us to talk about the canonical structure of differentiable stratified space on the orbispace (an object analogous to a separated stack in algebraic geometry) presented by the proper Lie groupoid. The canonical smooth structure on an orbispace is studied mainly via Spallek’s framework of differentiable spaces, and two alternative frameworks are then presented. For the canonical stratification on an orbispace, we extend the similar theory coming from proper Lie group actions. We make no claim to originality. The goal of these notes is simply to give a complementary exposition to those available and to clarify some subtle points where the literature can sometimes be confusing, even in the classical case of proper Lie group actions.
URI: http://hdl.handle.net/10316/45286
Other Identifiers: 10.1007/s11005-017-1011-6
DOI: 10.1007/s11005-017-1011-6
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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