Geodesic
A loop theorem/Dehn’s lemma for some orbifolds
Barnard, Josh1
1Department of Mathematics & Statistics, University of South Alabama, ILB 325, 307 North University Blvd, Mobile AL 36688, USA
Algebraic and Geometric Topology, Tome 11 (2011) no. 5, pp. 2815-2827
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The equivariant loop theorem implies the existence of a loop theorem/Dehn’s lemma for 3–orbifolds that are good (covered by a 3–manifold). In this note we prove a loop theorem/Dehn’s lemma for any locally orientable 3–orbifold (good or bad) whose singular set is labeled with powers of 2. The proof is modeled on the standard tower construction.

DOI : 10.2140/agt.2011.11.2815
Classification : 57M35
Keywords: loop Theorem, Dehn's Lemma, $3$–orbifold

Barnard, Josh  1

1 Department of Mathematics & Statistics, University of South Alabama, ILB 325, 307 North University Blvd, Mobile AL 36688, USA 
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Barnard, Josh. A loop theorem/Dehn’s lemma for some orbifolds. Algebraic and Geometric Topology, Tome 11 (2011) no. 5, pp. 2815-2827. doi: 10.2140/agt.2011.11.2815

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[4] Y Takeuchi, M Yokoyama, PL-least area $2$–orbifolds and its applications to $3$–orbifolds, Kyushu J. Math. 55 (2001) 19

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