Presentations of 3-manifolds arising from vector fields

Percell, Peter

doi:10.1090/S0002-9947-1976-0407857-X

Presentations of $3$-manifolds arising from vector fields
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Trans. Amer. Math. Soc. 221 (1976), 361-377 Request permission

Abstract:

A method is given for constructing a smooth, closed, orientable 3-manifold from the information contained in a combinatorial object called an abstract intersection sequence. An abstract intersection sequence of length n is just a cyclic ordering of the set $\{ \pm 1, \ldots , \pm n\}$ plus a map $\nu :\{ 1, \ldots ,n\} \to \{ \pm 1\}$. It is shown that up to diffeomorphism every closed, connected, orientable 3-manifold can be constructed by the method. This is proved by showing that compact, connected, orientable 3-manifolds with boundary the 2-sphere admit vector fields of a certain type. The intersection sequences arise as descriptions of the vector fields.

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Properly nested presentations of

manifolds

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