Homotopy self-equivalences of 4-manifolds with PD2 fundamental group

Abstract

Based on the approach of Hambleton and Kreck, an explicit description of the group of homotopy classes of homotopy self-equivalences of an orientable 4-manifold is obtained when the fundamental group of the manifold is a two-dimensional Poincaré duality group. As a byproduct, a classification of such four-manifolds up to s-cobordism is obtained by using the modified surgery theory of Kreck.

On minimal Poincaré $4$-complexes

“…Self-homotopy equivalences were studied by various authors (see [12] and references there). Pamuk's method can be used to calculate Aut(X ≻ P ).…”