The equivariant loop theorem implies the existence of a loop theorem/Dehn’s lemma for –orbifolds that are good (covered by a –manifold). In this note we prove a loop theorem/Dehn’s lemma for any locally orientable –orbifold (good or bad) whose singular set is labeled with powers of 2. The proof is modeled on the standard tower construction.
"A loop theorem/Dehn's lemma for some orbifolds." Algebr. Geom. Topol. 11 (5) 2815 - 2827, 2011. https://doi.org/10.2140/agt.2011.11.2815