Suborbifolds, quotients and transversality

TL;DR

This paper generalizes the concept of submanifolds to orbifolds, establishing conditions for subsets to inherit orbifold structures and extending classical constructions like embeddings and transversality to the orbifold context.

Contribution

It introduces a natural condition ensuring subsets of orbifolds carry canonical orbifold structures, broadening the scope of submanifold theory in orbifold geometry.

Findings

Defines a general condition for suborbifolds

Extends classical submanifold constructions to orbifolds

Demonstrates the approach with embeddings and group actions

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.