# On the Gray index conjecture for phantom maps - Mathematics > Algebraic Topology

Abstract: We study the Gray index of phantom maps, which is a numerical invariant ofphantom maps. It is conjectured that the only phantom map with infinite Grayindex between finite-type spaces is the constant map. We disprove thisconjecture by constructing a counter example. We also prove that thisconjecture is valid if the target spaces of phantom maps are restricted tosimply connected finite complexes.As an application of the counter example we show that $\SNT^{\infty}X$ canbe non-trivial for some space $X$ of finite type.

Author: Kouyemon Iriye Osaka Prefecture University

Source: https://arxiv.org/