## Presentations of $3$-manifolds arising from vector fields

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- by Peter Percell PDF
- 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*3-

*manifolds*(to appear).

## Additional Information

- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**221**(1976), 361-377 - MSC: Primary 57D25; Secondary 58C25, 57A10
- DOI: https://doi.org/10.1090/S0002-9947-1976-0407857-X
- MathSciNet review: 0407857