The Borsuk-Ulam property for cyclic groups
Keywords
Equivariant maps, the Euler class, G-categoryAbstract
An orthogonal representation $V$ of a group $G$ is said to have the Borsuk-Ulam property if the existence of an equivariant map $f:S(W) \rightarrow S(V)$ from a sphere of representation $W$ into a sphere of representation $V$ implies that $\dim W \leq \dim V$. It is known that a sufficient condition for $V$ to have the Borsuk-Ulam property is the nontriviality of its Euler class ${\text {\bf e}}(V)\in H^{*} (BG;\mathcal R)$. Our purpose is to show that ${\text {\bf e}}(V) \neq 0 $ is also necessary if $G$ is a cyclic group of odd and double odd order. For a finite group $G$ with periodic cohomology an estimate for $G$-category of a $G$-space $X$ is also derived.Downloads
Published
2000-09-01
How to Cite
1.
IZYDOREK, Marek and MARZANTOWICZ, Wacław. The Borsuk-Ulam property for cyclic groups. Topological Methods in Nonlinear Analysis. Online. 1 September 2000. Vol. 16, no. 1, pp. 65 - 72. [Accessed 20 April 2024].
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