s-Cobordism Classification of 4-Manifolds Through the Group of Homotopy Self-equivalences

The aim of this paper is to give an s-cobordism classification of topological 4 manifolds in terms of the standard invariants using the group of homotopy self-equivalences. Hambleton and Kreck constructed a braid to study the group of homotopy self-equivalences of 4-manifolds. Using this braid together with the modified surgery theory of Kreck, we give an s-cobordism classification for certain 4-manifolds with fundamental group π, such that cd π ≤ 2.