Borsuk-Ulam theorems for elementary abelian 2-groups
DOI:
https://doi.org/10.12775/TMNA.2022.042Słowa kluczowe
Borsuk-Ulam theorem, Bourgin-Yang theorem, equivariant mapping, Euler classAbstrakt
Let $G$ be a fct Lie group and let $U$ and $V$ be finite-dimensional real $G$-modules with $V^G=0$. A theorem of Marzantowicz, de Mattos and dos Santos estimates the covering dimension of the zero-set of a $G$-map from the unit sphere in $U$ to $V$ when $G$ is an elementary abelian $p$-group for some prime $p$ or a torus. In this note, the classical Borsuk-Ulam theorem will be used to give a refinement of their result estimating the dimension of that part of the zero-set on which an elementary abelian $p$-group $G$ acts freely or a torus $G$ acts with finite isotropy groups. The methods also provide an easy answer to a question raised in \cite{DM}.Bibliografia
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Prawa autorskie (c) 2023 Michael C. Crabb
Utwór dostępny jest na licencji Creative Commons Uznanie autorstwa – Bez utworów zależnych 4.0 Międzynarodowe.
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