On the notions of suborbifold and orbifold embedding

Borzellino, Joseph E¹ ; Brunsden, Victor²

¹Department of Mathematics, California Polytechnic State University, 1 Grand Avenue, San Luis Obispo, CA 93407, USA
²Department of Mathematics and Statistics, Penn State Altoona, 3000 Ivyside Park, Altoona, PA 16601, USA

Algebraic and Geometric Topology, Tome 15 (2015) no. 5, pp. 2787-2801

Résumé

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.

Détail

DOI : 10.2140/agt.2015.15.2789

Classification : 57R18, 57R35, 57R40
Keywords: orbifold, embeddings, suborbifold

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