## Open book decompositions versus prime factorizations of closed, oriented 3-manifolds

*Ghiggini, Paolo*;

*Lisca, Paolo*;

- Subject: 57N10, 57M25 | Mathematics - Geometric Topologyarxiv: Mathematics::Geometric Topology

Let $M$ be a closed, oriented, connected 3--manifold and $(B,\pi)$ an open book decomposition on $M$ with page $\Sigma$ and monodromy $\varphi$. It is easy to see that the first Betti number of $\Sigma$ is bounded below by the number of $S^2\times S^1$--factors in the p... View more

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