The homology of cyclic products

Abstract

I will present here a method for calculating the homology, with arbitrary coefficients, of n-fold cyclic products for all n, not merely for the case where n is a prime. The construction used is natural up to homotopy and so permits the determination of the map of this homology induced by any map of the original space. In particular, if we have a diagonal chain map for the original space, we can find one for the cyclic product and so can compute cup products. In applying this method, it is not necessary to assume that the spaces involved are finite complexes. In fact, the method applies to any semisimplicial complex, finite or not. In the case where the ground ring is a field, I will give an explicit natural

Locations

• Project Euclid (Cornell University) - View - PDF
• Transactions of the American Mathematical Society - View - PDF