Branchfolds, varietà coniche razionali e il problema di Cheeger-Simons

Roughly speaking, an m-dimensional branchfold is a space covered by open sets U admitting two regular branched coverings V ← P → U, with P a polyhedron and V an open subset of Rm, rather than only one V → U as in the orbifold case. After recalling the main definitions, constructions and results in the theory of branchfolds, we will explain why and how such spaces can be useful to shed some light on the Cheeger-Simons problem of whether the volume of a compact spherical conifold with rational angles is a rational multiple of the volume of the m-sphere.