Presentations of -manifolds arising from vector fields

Author:
Peter Percell

Journal:
Trans. Amer. Math. Soc. **221** (1976), 361-377

MSC:
Primary 57D25; Secondary 58C25, 57A10

MathSciNet review:
0407857

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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 plus a map . 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1976-0407857-X

Keywords:
Presentation,
3-manifold,
intersection sequence,
generic transient vector field,
branched manifold

Article copyright:
© Copyright 1976
American Mathematical Society