Abstract
DIHOMOLOGY is a homology theory based on the use of pairs of cells instead of single cells as in classical homology. The pairs considered have some specified geometrical or topological relationship, which is called a facing relation. The resulting double complex is handled by means of spectral sequences. The technique is dual in a certain sense to the taking of tensor products over a ring. For if K, L are A-complexes we feed the A-structure into K®L by forming the quotient complex K® AL. So in dihomology we feed the facing relation into K®L by forming a sub- complex. There is no reason for restricting ourselves to pairs of cells, and the theory extends quite happily to three or more. In fact in the proof of the last theorem in the second paper (12) we have to use a quintuple facing relation.
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