Handle decompositions of simply-connected five-manifolds. II (Q1343446)

The main result of the paper under review (Theorem 3) asserts that the Barden handle decomposition of a closed simply connected smooth or PL 5-manifold \(M\) is geometrically diagonal: All indicence indices of 2- and 3-handles of the Barden handle decomposition of \(M\) are geometrically diagonal. The result is obtained by proving and making use of a theorem (Theorem 2) which gives the geometric description of the Wall diffeomorphisms for some simply connected 4-manifolds. The paper applies the notions and techniques of the first part of this paper (see the review above) which allow to describe properties of the elementary 4-manifolds, the standard 5-manifolds, and handle decompositions of 5-manifolds.