Canonical Sphere Bases for Simplicial and Cubical Complexes

03/14/2023

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by   Paul C. Kainen, et al.

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Sphere-bases are constructed for the ℤ_2 vector space formed by the k-dimensional subcomplexes, of n-simplex (or n-cube), for which every (k-1)-face is contained in a positive even number of k-cells; addition is symmetric difference of the corresponding sets of k-cells. The bases consist of the boundaries of an algorithmically-specified family of k+1-simplexes or k+1-cubes. Geometric properties of these bases are investigated.