Differential Geometry and its Applications
Final Published Version
We introduce a novel and constructive definition of gluing data, and give the first rigorous proof that a universal manifold satisfying the Hausdorff condition 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. We give a construction for building a set of gluing data from any simplicial surface in R3. This construction is an improvement of the construction given in Siqueira et al. (2009), where the results were stated without proof. We also give a complete proof of the correctness of this construction making use of the crucial “property A.” The above results enable us to develop a methodology that explicitly yields manifolds in Rn arising in several graphics and engineering applications.
Copyright 2012 Elsevier. The published version of this article is available here: http://dx.doi.org/10.1016/j.difgeo.2012.09.002
Gallier, J., D. Xu, and M. Siqueira 2012. Parametric pseudo-manifolds. Differential Geometry and its Applications 30.6: 702-736.