2021/03/25 by Basak, Biplab, Binjola, Manisha
#05E45 #57M15 #57M50 #57Q05 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Primary 57Q15 #Secondary 05C15
paper · doi:10.48550/arxiv.2103.13602
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 ≤ 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 ℤ, we have constructed a handle decomposition for M as one of the following types: (1) one 0-handle, two 1-handles, 1+β2(M) 2-handles, one 3-handle and one 4-handle, (2) one 0-handle, one 1-handle, β2(M) 2-handles, one 3-handle and one 4-handle, where β2(M) denotes the second Betti number of manifold M with ℤ coefficients.