Handle decompositions for a class of closed orientable PL 4-manifolds

In this article, we study a class of closed connected orientable PL 4-manifolds admitting a semi-simple crystallization and which have an infinite cyclic fundamental group. We show that the manifold in the class admits a handle decomposition in which the number of 2-handles depends upon its second Betti number and other h-handles ( $$h \le 4$$ h ≤ 4 ) are at most 2. More precisely, our main result is the following. For a closed connected orientable PL 4-manifold having a semi-simple crystallization with the fundamental group as $$\mathbb {{Z}}$$ Z , we have constructed a handle decomposition for M as one of the following types: (1) one 0-handle, two 1-handles, $$1+\beta _2(M)$$ 1 + β 2 ( M ) 2-handles, one 3-handle and one 4-handle, (2) one 0-handle, one 1-handle, $$\beta _2(M)$$ β 2 ( M ) 2-handles, one 3-handle and one 4-handle, where $$\beta _2(M)$$ β 2 ( M ) denotes the second Betti number of manifold M with $$\mathbb {Z}$$ Z coefficients.