Canonical sphere bases for simplicial and cubical complexes.

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. Properties of the bases are investigated. [ABSTRACT FROM AUTHOR]