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