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

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

2010-08-06

arxiv.org/abs/1008.1134v1

Topology Proceedings, 36 (2010), 249-253

Mathematics

Algebraic Topology

4 pages, appeared in Topology Proceedings

Scientific paper

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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