分野別セミナー

Let $G=Z_{p^k}$ be a cyclic group of prime power order and let $V$ and $W$ be orthogonal representations of $G$ with $V^{G}= W^{G}=¥{0¥}$. Let $S(V)$ be the sphere of $V$ and suppose $f:S(V)¥to W$ is a $G$-equivariant mapping. In this seminar, we will consider the problem to estimate the dimension of the set $f^{-1}¥{0¥}$ in terms of $V$ and $W$. This is an extension of the Bourgin-Yang theorem to this class of groups.

Joint work with Waclaw Marzantowicz and Edivaldo L. dos Santos