The Strong Coarse Homotopy Groups

Abstract

In this Article the cofibration category machinery (see [1], [2]) is used to define strong coarse homotopy groups (for preliminaries see [3],[4],[5],[6]) in the pointed quotient coarse category PQcrs via the notion of strong coarse homotopy as defined in [7] which we proved to be a Baues cofibration category in [8], [9]. In general, our definition is the same as the abstract definition. Later we also show that there is a surjective homomorphism between these groups and the n-dimensional coarse spheres.