Date of this Version
Jean H. Gallier, Dianna Xu, and Marcelo Siqueira, "Parametric Pseudo-Manifolds", . December 2011.
We introduce a novel and constructive definition of gluing data, and prove that a universal manifold can always be constructed from any set of gluing data. We also present a class of spaces called parametric pseudo-manifolds, which under certain conditions are manifolds embedded in Rn and defined from sets of gluing data. The combination of both definitions is equivalent to a constructive definition of manifolds. They also enable us to develop constructions that explicitly yield manifolds in Rn arising in several graphics and engineering applications.
Date Posted: 19 July 2012