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

Biplab Basak () and Manisha Binjola ()
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Biplab Basak: Indian Institute of Technology Delhi
Manisha Binjola: Indian Institute of Technology Delhi

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 4, 1166-1172

Abstract: Abstract 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.

Keywords: PL-manifolds; Crystallizations; Regular genus; Handle decomposition; Primary 57Q15; Secondary 05C15; 05E45; 57Q05; 57M15; 57M50 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00417-y

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