Every 3-manifold admits a structurally stable nonsingular flow with three basic sets

Yu, Bin

doi:10.1090/proc/13122

Every $3$-manifold admits a structurally stable nonsingular flow with three basic sets
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by Bin Yu

Proc. Amer. Math. Soc. 144 (2016), 4949-4957

DOI: https://doi.org/10.1090/proc/13122

Published electronically: May 3, 2016

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Abstract:

This paper is devoted to proving that every closed orientable $3$-manifold admits a simple Smale flow $X_t$. Here a simple Smale flow is a structurally stable nonsingular flow whose chain recurrent set is composed of a periodic orbit attractor, a periodic orbit repeller and a transitive saddle invariant set, i.e., a saddle basic set.

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