A splitting theorem for homotopy equivalent smooth 4-manifolds

Abstract

We prove a decomposition theorem for closed connected homotopy equivalent smooth four-manifolds, which partially extends a recent result of [2] to the non-simply connected case. Then we study the question of when a homotopy equivalence between closed smooth 4-manifolds is homotopic to a topological homeomorphism. In particular, we obtain a new proof of the well-known uniqueness of closed aspherical smooth 4-manifolds with good fundamental groups.

Keywords

• four-manifolds
• homotopy equivalences
• immersions
• homotopy type
• homeomorphism type
• covering maps
• aspherical manifolds