2022/08/09 by Pengcheng Li, Li, Pengcheng
Mathematics · Medicine · #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #Advanced Topology and Set Theory
paper · pdf · doi:10.48550/arxiv.2208.04776
The self-closeness number of a CW-complex is a homotopy invariant defined by the minimal number n such that every self-maps of X which induces automorphisms on the first n homotopy groups of X is a homotopy equivalence. In this article we study the self-closeness numbers of finite Cartesian products, and prove that under certain conditions (called reducibility), the self-closeness number of product spaces equals to the maximum of self-closeness numbers of the factors. A series of criteria for the reducibility are investigated, and the results are used to determine self-closeness numbers of product spaces of some special spaces, such as Moore spaces, Eilenberg-MacLane spaces or atomic spaces.