A loop theorem/Dehn's lemma for some orbifolds

Abstract

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.