Polyhedral representations of discrete differential manifolds
نویسنده
چکیده
Any discrete differential manifold M (finite set endowed with an algebraic differential calculus) can be represented by appropriate polyhedron P(M). This representation demonstrates the adequacy of the calculus of discrete differential manifolds and links this approach with that based on finitary substitutes of continuous spaces introduced by R.D.Sorkin.
منابع مشابه
Generating Discrete Trace Transition System of a Polyhe-dral Invariant Hybrid Automaton
Supervisory control and fault diagnosis of hybrid systems need to have complete information about the discrete states transitions of the underling system. From this point of view, the hybrid system should be abstracted to a Discrete Trace Transition System (DTTS) and represented by a discrete mode transition graph. In this paper an effective method is proposed for generating discrete mode trans...
متن کاملMirror Symmetry via Logarithmic Degeneration Data I Mark Gross and Bernd Siebert
Introduction. 2 1. Affine Manifolds 9 1.1. Affine Manifolds and Invariants 9 1.2. Affine manifolds with singularities 15 1.3. Polyhedral decompositions 18 1.4. The discrete Legendre transform 33 1.5. Positivity and simplicity 39 2. From polyhedral decompositions to algebraic spaces 48 2.1. The cone picture 49 2.2. The fan picture 52 3. Logarithmic structures 79 3.
متن کاملA Result on Representations of Homology Manifolds by Finite Spaces
We prove a result relating the Euler characteristic of a polyhedral closed homology manifold to the finite space associated with a triangulation of the manifold. We then give a new proof that polyhedral closed homology manifolds have Euler characteristic 0.
متن کاملDiscrete Differential Geometry 655 Workshop : Discrete Differential Geometry
Discrete Differential Geometry is a broad new area where differential geometry (studying smooth curves, surfaces and other manifolds) interacts with discrete geometry (studying polyhedral manifolds), using tools and ideas from all parts of mathematics. This report documents the 29 lectures at the first Oberwolfach workshop in this subject, with topics ranging from discrete integrable systems, p...
متن کاملSobolev Spaces on Lie Manifolds and Polyhedral Domains
We study Sobolev spaces on Lie manifolds, which we define as a class of manifolds described by vector fields (see Definition 1.2). The class of Lie manifolds includes the Euclidean spaces Rn, asymptotically flat manifolds, conformally compact manifolds, and manifolds with cylindrical and polycylindrical ends. As in the classical case of Rn, we define Sobolev spaces using derivatives, powers of ...
متن کامل