On the notions of suborbifold and orbifold embedding

Joseph E. Borzellino, Victor Brunsden

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

The purpose of this article is to investigate the relationship between suborbifolds and orbifold embeddings. In particular, we give natural definitions of the notion of suborbifold and orbifold embedding and provide many examples. Surprisingly, we show that there are (topologically embedded) smooth suborbifolds which do not arise as the image of a smooth orbifold embedding. We are also able to characterize those suborbifolds that can arise as the images of orbifold embeddings. As an application, we show that a length-minimizing curve (a geodesic segment) in a Riemannian orbifold can always be realized as the image of an orbifold embedding.

Original languageEnglish (US)
Pages (from-to)2789-2803
Number of pages15
JournalAlgebraic and Geometric Topology
Volume15
Issue number5
DOIs
StatePublished - Nov 12 2015

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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