The \(\mathbb{F}_2\)-cohomology rings of \(\mathbb{S}ol^3\)-manifolds

J. A. Hillman

Abstract

We compute the rings \(H^*(N;\mathbb{F}_2)\) for \(N\) a closed \(\mathbb{S}ol^3\)-manifold, and then determine the Borsuk-Ulam indices \(BU(N,\phi)\) with \(\phi\not=0\) in \(H^1(N;\mathbb{F}_2)\).

Keywords: Borsuk-Ulam Theorem, cohomology, \(\mathbb{S}ol^3\)-manifold.

AMS Subject Classification: Primary 57M25.