Integral cohomology and detection of 𝑤-basic 2-groups

Abstract

Abstract. In this paper we compute the cohomology H * (G; Z w ) of all wbasic 2-groups (G, w) with integral coefficients twisted by the orientation character w. We also calculate appropriate restiction maps and thus prove that the cohomology of any w-basic group is detected by subgroups isomorphic to one of five types, and we provide a sample application of this main theorem.

Groups that act pseudofreely on S2×S2

“…Rather than interrupt the flow of that argument later, we discuss them here. The methods used to calculate these maps are described in [15]. Some of the specific maps are also described there, and most of the rest were worked in the course of a conversation with the author of that paper.…”

“…Determining which actually occurs requires a closer look at the Bockstein spectral sequence. Details are in [15]; our calculation later on actually only requires that each be an even multiple of c.…”