On the Inheritance of Orbifold Substructures
Joseph E. Borzellino, Victor Brunsden

TL;DR
This paper explores how orbifold substructures are inherited through a chain of orbifolds, revealing complexities and limitations in canonical inheritance and the role of saturation.
Contribution
It provides a detailed analysis of orbifold structure inheritance, introduces examples illustrating when inheritance is canonical or fails, and examines the concept of saturation in suborbifolds.
Findings
Canonical inheritance can fail in intermediate orbifolds.
When suborbifolds are embedded, canonical structures agree.
Saturation is a key property influencing inheritance.
Abstract
In a previous article, we defined a very flexible notion of suborbifold and characterized those suborbifolds which can arise as the images of orbifold embeddings. In particular, suborbifolds are images of orbifold embeddings precisely when they are saturated and split. This article addresses the problem of orbifold structure inheritance for three orbifolds . We identify an appealing but ultimately inadequate notion of an inherited canonical orbifold substructure. In particular, we give a concrete example where the orbifold structure of is canonically inherited from , and the orbifold structure of is canonically inherited from , but the orbifold structure of is not canonically inherited from . On the other hand, it is easy to see that when is…
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