Elementary Orbifold Differential Topology

Abstract

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.

10 pages, 2 figures

References in corpus (1)

• The Stratified Structure of Spaces of Smooth Orbifold Mappings

Cited by in corpus (7)

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• Three-orbifolds with positive scalar curvature
• The Steenrod problem for orbifolds and polyfold invariants as intersection numbers
• Suborbifolds and groupoid embeddings