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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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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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