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Transactions of the American Mathematical Society

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

 

 

Templates and train tracks


Author: George Frank
Journal: Trans. Amer. Math. Soc. 308 (1988), 765-784
MSC: Primary 58F15; Secondary 57M15, 57N10, 58F25
MathSciNet review: 951627
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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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DOI: https://doi.org/10.1090/S0002-9947-1988-0951627-9
Article copyright: © Copyright 1988 American Mathematical Society