Script Geometry

Abstract

In this paper we describe the foundation of a new kind of discrete geometry and calculus called Script Geometry. It allows to work with more general meshes than classic simplicial complexes. We provide the basic definitions as well as several examples, like the Klein bottle and the projective plane. Furthermore, we also introduce the corresponding Dirac and Laplace operators which should lay the groundwork for the development of the corresponding discrete function theory. Mathematics Subject Classification (2010). 30G35, 65N30, 58A14.