A topological version of Hedetniemi's conjecture for equivariant spaces

Abstract

A topological version of the famous Hedetniemi conjecture says: The mapping index of the Cartesian product of two $\mathbb{Z}/2$-spaces is equal to the minimum of their $\mathbb{Z}/2$-indexes. The main purpose of this article is to study the topological version of the Hedetniemi conjecture for $G$-spaces. Indeed, we show that the topological Hedetniemi conjecture cannot be valid for general pairs of $G$-spaces. More precisely, we show that this conjecture can possibly survive if the group $G$ is either a cyclic $p$-group or a generalized quaternion group whose size is a power of 2.

9 pages, 1 figure; comments are welcome

References in corpus (1)

• On inverse powers of graphs and topological implications of Hedetniemi's conjecture