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Embeddings of 3-manifolds in 5 dimensinal manifolds

  • Dr. Suhas Jaykumar Pandit, Assistant Professor, Department of Mathematics, IIT Madras

We discuss embeddings of 3–manifolds via open books. First we show that every open book of every closed orientable 3–manifold admits an open book embedding in any open book decompistion of $S^2 X S^3$ and twisted $S^2X S^3$ with the page a disk bundle over $S^2$ and monodromy the identity. We then use open book embeddings to reprove Hrirsch's that every closed orientable 3–manifold embeds in $S^5$.