A Topological Version of Hedetniemi’s Conjecture for Equivariant Spaces

A topological version of the famous Hedetniemi conjecture says: The mapping index of the Cartesian product of two Z/ 2 - spaces is equal to the minimum of their 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.