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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Templates and train tracks
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by George Frank PDF
Trans. Amer. Math. Soc. 308 (1988), 765-784 Request permission

Abstract:

Within the context of Smale flows on compact manifolds, this article deals with a relationship between abstract templates, branched $1$-manifolds (train tracks), and laminations representing unstable separatrices of basic sets. We show that an abstract template, the richest in information of the above three entities, determines a member of each of the remaining two groups, and partial determinations in other directions are developed. As a result of this relationship, an obstruction to the realization of certain abstract templates in nonsingular Smale flows on homology $3$-spheres is raised.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 308 (1988), 765-784
  • MSC: Primary 58F15; Secondary 57M15, 57N10, 58F25
  • DOI: https://doi.org/10.1090/S0002-9947-1988-0951627-9
  • MathSciNet review: 951627