A simple proof of the Borsuk-Ulam theorem for Z_p-actions

Mahender Singh

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arXiv · 1008.1134

A simple proof of the Borsuk-Ulam theorem for Z_p-actions

Mahender Singh

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Abstract

In this note, we give a simple proof of the Borsuk-Ulam theorem for $Z_p$-actions. We prove that, if $S^n$ and $S^m$ are equipped with free $Z_p$-actions (p prime) and $f: S^n \to S^m$ is a $Z_p$-equivariant map, then $n \leq m$.

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BibTeX RIS

Mahender Singh. 2010-08-06. A simple proof of the Borsuk-Ulam theorem for Z_p-actions. https://arxiv.org/abs/1008.1134

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