On the notions of suborbifold and orbifold embedding

Joseph E. Borzellino, Victor Brunsden

Research output: Contribution to journalArticle

4 Citations (Scopus)

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

Fingerprint

Orbifold
Geodesic
Curve

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

Borzellino, Joseph E. ; Brunsden, Victor. / On the notions of suborbifold and orbifold embedding. In: Algebraic and Geometric Topology. 2015 ; Vol. 15, No. 5. pp. 2789-2803.
@article{bf595ad9e09843809ede4ae4c9a1b13f,
title = "On the notions of suborbifold and orbifold embedding",
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.",
author = "Borzellino, {Joseph E.} and Victor Brunsden",
year = "2015",
month = "11",
day = "12",
doi = "10.2140/agt.2015.15.2789",
language = "English (US)",
volume = "15",
pages = "2789--2803",
journal = "Algebraic and Geometric Topology",
issn = "1472-2747",
publisher = "Agriculture.gr",
number = "5",

}

On the notions of suborbifold and orbifold embedding. / Borzellino, Joseph E.; Brunsden, Victor.

In: Algebraic and Geometric Topology, Vol. 15, No. 5, 12.11.2015, p. 2789-2803.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On the notions of suborbifold and orbifold embedding

AU - Borzellino, Joseph E.

AU - Brunsden, Victor

PY - 2015/11/12

Y1 - 2015/11/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84947915367&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84947915367&partnerID=8YFLogxK

U2 - 10.2140/agt.2015.15.2789

DO - 10.2140/agt.2015.15.2789

M3 - Article

AN - SCOPUS:84947915367

VL - 15

SP - 2789

EP - 2803

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

SN - 1472-2747

IS - 5

ER -