A new approach for data transmission system on topological surfaces

this work introduces a new data transmission system in which the main blocks, coding, modulation and channel are designed on a riemannian manifolds. an intrinsic algebraic structure to the manifolds (surface), the homology group will be used to compose an error corrector code, a partition on the surface extracted from the embedding of a graph, which will compose the modulation design, and the channel design is the result of an association rule applied to the embedded graph. mathematical subject classification: primary: 06b10; secondary: 06d05.