2005/04/26 by Gordon Chalmers, Chalmers, Gordon
Computer Science · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #FOS: Physical sciences #General Physics (physics.gen-ph) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.physics/0504188
8 pages, LaTeX
arxiv created 2005/04/26 · openalex publication_date 2005/04/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The polytopic definition introduced recently describing the topology of manifolds is used to formulate a generating function pertinent to its topological properties. In particular, a polynomial in terms of one variable and a tori underlying this polynomial may be defined that generates an individual cohomological count. This includes the de Rham complex for example, as well as various index theorems by definition such as homotopy. The degree of the polynomials depends on the volume used to define the region parameterizing the manifolds; its potentially complex form and L-series is not presented in this work. However, the polynomials and the relevant torii uniformize the topological properties in various dimensions; in various dimensions this is interesting in view of known topologies.