Effective chain complexes for twisted products. (Q2846607)

This article is concerned with the reduction of chain complexes to effective chain complexes. There are essentially two new results. The first result uses the basic perturbation lemma and reductions in the component complexes to give conditions for the existence of a reduction of the twisted Cartesian product complex to an effective complex. A related result gives conditions for a twisted Cartesian product to be strongly equivalent to an effective chain complex using strong equivalences of the component complexes.