Suborbifolds, quotients and transversality
arXiv:1512.08937 · doi:10.1016/j.topol.2017.03.011
Abstract
Inspired by work of Borzellino and Brunsden, we generalize the notion of a submanifold identifying a natural and sufficiently general condition which guarantees that a subset of an (effective) orbifold carries itself a canonical induced orbifold structure. We illustrate the strength of this approach generalizing typical constructions of submanifolds to the orbifold setting using embeddings, proper group actions and the idea of transversality.
16 pages; minor corrections, relation to earlier suborbifold notions clarified; to appear in Topology and its Applications