## 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.

: Primary 57M25.

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 Tuesday, October 9, 2012