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On the notions of
suborbifold and orbifold embedding
Joseph E Borzellino and Victor Brunsden |
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Algebraic & Geometric Topology 15 (2015) 2787–2801
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Abstract |
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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. |
Keywords
orbifold, embeddings, suborbifold
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Mathematical Subject Classification 2010
Primary: 57R18
Secondary: 57R35, 57R40
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References |
Publication
Received: 17 June 2014
Revised: 2 December 2014
Accepted: 14 January 2015
Published: 10 December 2015
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Authors |
| Joseph E Borzellino | |
| Department of Mathematics California Polytechnic State University 1 Grand Avenue San Luis Obispo, CA 93407 USA |
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| Victor Brunsden | |
| Department of Mathematics and
Statistics Penn State Altoona 3000 Ivyside Park Altoona, PA 16601 USA |
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