On the Gray index conjecture for phantom maps |
| |
Authors: | Kouyemon Iriye |
| |
Institution: | Department of Mathematics and Information Sciences, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan |
| |
Abstract: | We study the Gray index, a numerical invariant for phantom maps. It has been conjectured that the only phantom map between finite-type spaces with infinite Gray index is the constant map. We disprove this conjecture by constructing a counter example. We also prove that this conjecture is valid if the target spaces of the phantom maps are restricted to being simply connected finite complexes.As a result of the counter example, we can show that SNT∞(X) can be non-trivial for some space X of finite type. |
| |
Keywords: | Phantom map Gray index SNT set |
本文献已被 ScienceDirect 等数据库收录! |
|