Elementary orbifold differential topology

Joseph E. Borzellino, Victor Brunsden

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Taking an elementary and straightforward approach, we develop the concept of a regular value for a smooth map f:O→P between smooth orbifolds O and P. We show that Sard's theorem holds and that the inverse image of a regular value is a smooth full suborbifold of O. We also study some constraints that the existence of a smooth orbifold map imposes on local isotropy groups. As an application, we prove a Borsuk no retraction theorem for compact orbifolds with boundary and some obstructions to the existence of real-valued orbifold maps from local model orbifold charts.

Original languageEnglish (US)
Pages (from-to)3583-3589
Number of pages7
JournalTopology and its Applications
Issue number17
StatePublished - Nov 1 2012

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


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