The ${\mathbb{F}}_2$-cohomology rings of $\mathbb{S}o{l}^3$-manifolds

J. A. Hillman

Abstract

We compute the rings $H^{\ast }(N;{\mathbb{F}}_2)$ for $N$ a closed $\mathbb{S}o{l}^3$-manifold, and then determine the Borsuk-Ulam indices $BU(N,\varphi )$ with $\varphi \ne 0$ in $H^1(N;{\mathbb{F}}_2)$.

Keywords: Borsuk-Ulam Theorem, cohomology, $\mathbb{S}o{l}^3$-manifold.

AMS Subject Classification: Primary 57M25.