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Journal of the Ramanujan Mathematical Society

Volume 36, Issue 3, September 2021  pp. 243–250.

Embeddings of 3-manifolds via open books

Authors:  Dishant M. Pancholi, Suhas Pandit and Kuldeep Saha
Author institution:Institute of Mathematical Sciences, IV, Cross Road, CIT Campus, Taramani, Chennai 600~133, Tamilnadu, India

Summary:  We prove that every open book decomposition of a closed orientable 3-manifold admits open book embedding in every open book decomposition of S{2} × S{3} and S{2} × S{3} with page a disk bundle over S{2} and monodromy the identity map. As an application of our methods, we give a new proof of a classical result of Hirsch which says that every closed orientable 3-manifold embeds in S{5}.

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