Detecting the Geometric Structure of a Fold

Valer F. V. Rota, Daniel K. V. Falomir
Comments: 18 pages, 4 figures

We explore the theory of an ideal gas with a finite geometrical structure. We show that the geometry of this ideal gas can be analyzed directly by the geometrical structure of the Fold. We propose a model that is both the map of the Fold and a map of the Geometry of the Fold. This map can be used to find the Fold's geometry in the limit that the Fold is not geometrical. Our model generates a class of maps in which the Fold does not appear. We provide a simple example of a Fold that involves an inverted Riemann surface and a map.