ON SIKORA'S SPECTRAL SEQUENCES

Abstract

In his study of Poincaré duality of a space X acted on by a group G, Sikora uses three spectral sequences which he calls the Leray, the Leray–Serre and the Swan spectral sequences. I show that, if G is discrete and X is compact and Hausdorff, then the Alexander–Spanier cohomology versions of these three spectral sequences are isomorphic. If X is also HLC, then all versions of them are isomorphic.