Canonical sphere bases for simplicial and cubical complexes

Abstract

Sphere-bases are constructed for the [Formula: see text] vector space formed by the [Formula: see text]-dimensional subcomplexes, of [Formula: see text]-simplex (or [Formula: see text]-cube), for which every [Formula: see text]-face is contained in a positive even number of [Formula: see text]-cells; addition is symmetric difference of the corresponding sets of [Formula: see text]-cells. The bases consist of the boundaries of an algorithmically-specified family of [Formula: see text]-simplexes or [Formula: see text]-cubes. Properties of the bases are investigated.