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arXiv · 1410.0142

Involutions on sapphire Sol 3-manifolds and the Borsuk-Ulam theorem for maps into $R^n$

Alexandre Paiva Barreto·Daciberg Lima Gonçalves·Daniel Vendrúscolo
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Abstract

For each sapphire Sol $3$-manifold, we classify the free involutions. For each triple $(M, τ; R^n)$ where $M$ is a sapphire Sol $3$-manifold and $τ$ is a free involution, we show if $(M, τ; R^n)$ has the Borsuk-Ulam property or not. It is known that for $n>3$ the Borsuk-Ulam property does not hold independent of the involution, so we provide a classification when $n=2$ and $3$.

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Alexandre Paiva Barreto, Daciberg Lima Gonçalves, Daniel Vendrúscolo. 2014-11-13. Involutions on sapphire Sol 3-manifolds and the Borsuk-Ulam theorem for maps into $R^n$. https://arxiv.org/abs/1410.0142

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