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On the notions of suborbifold and orbifold embedding

Joseph E Borzellino and Victor Brunsden

Algebraic & Geometric Topology 15 (2015) 2787–2801

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.

orbifold, embeddings, suborbifold
Mathematical Subject Classification 2010
Primary: 57R18
Secondary: 57R35, 57R40
Received: 17 June 2014
Revised: 2 December 2014
Accepted: 14 January 2015
Published: 10 December 2015
Joseph E Borzellino
Department of Mathematics
California Polytechnic State University
1 Grand Avenue
San Luis Obispo, CA 93407
Victor Brunsden
Department of Mathematics and Statistics
Penn State Altoona
3000 Ivyside Park
Altoona, PA 16601