The F2 Cohomology of Sol^3-Manifolds

TL;DR

This paper calculates the mod 2 cohomology rings of closed Sol^3-manifolds and determines their Borsuk-Ulam indices, providing new insights into their topological properties.

Contribution

It provides the first explicit computation of the mod 2 cohomology rings and Borsuk-Ulam indices for closed Sol^3-manifolds, advancing understanding of their topological invariants.

Findings

Computed cohomology rings H^*(N;F_2) for Sol^3-manifolds

Determined Borsuk-Ulam indices for these manifolds

Enhanced understanding of topological invariants of Sol^3-manifolds

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 $H^1(N;\mathbb{F}_2)$.