Quasi-Boolean groups

TL;DR

This paper characterizes the maximal pro-2 quotients of real projective groups through various equivalent methods, including presentations and cohomological properties, enabling explicit reconstruction from cohomology rings.

Contribution

It provides new presentations and cohomological characterizations of pro-2 real projective groups, facilitating their explicit reconstruction from cohomology data.

Findings

Equivalent characterizations of maximal pro-2 quotients

Presentation of pro-2 groups via generators and relations

Reconstruction from mod 2 cohomology rings

Abstract

We give several equivalent characterisations of the maximal pro-2 quotients of real projective groups. In particular, for pro-2 real projective groups we provide a presentation in terms of generators and relations, and a purely cohomological characterisation. As a consequence we explicitly reconstruct such groups from their mod 2 cohomology rings.