17 citations · 42 across the 7 of their papers we have counts for
6 papers · 1 filter
On the Inheritance of Orbifold Substructures
Joseph E. Borzellino, Victor Brunsden
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, su…
On the notions of suborbifold and orbifold embedding
Joseph E. Borzellino, Victor Brunsden
The purpose of this article is to investigate the relationship between suborbifolds and orbifold embeddings. In particular, we give natural definitions of the notion of suborbifold…
Elementary Orbifold Differential Topology
Joseph E. Borzellino, Victor Brunsden
Taking an elementary and straightforward approach, we develop the concept of a regular value for a smooth map f: O -> P between smooth orbifolds O and P. We show that Sard's theore…
The Stratified Structure of Spaces of Smooth Orbifold Mappings
Joseph E. Borzellino, Victor Brunsden
We consider four notions of maps between smooth C^r orbifolds O, P with O compact (without boundary). We show that one of these notions is natural and necessary in order to uniquel…
A manifold structure for the group of orbifold diffeomorphisms of a smooth orbifold
Joseph E. Borzellino, Victor Brunsden
For a compact, smooth C^r orbifold (without boundary), we show that the topological structure of the orbifold diffeomorphism group is a Banach manifold for finite r \ge 1 and a Fre…
On the existence of infinitely many closed geodesics on orbifolds of revolution
Joseph E. Borzellino, Christopher R. Jordan-Squire, Gregory C. Petrics +1
Using the theory of geodesics on surfaces of revolution, we introduce the period function. We use this as our main tool in showing that any two-dimensional orbifold of revolution h…