Poincaré flows

Schwartzman, Sol

doi:10.1090/S0002-9939-97-04032-X

Poincaré flows
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Proc. Amer. Math. Soc. 125 (1997), 2493-2500 Request permission

Abstract:

We study flows on a compact metric space $X$ with the property that corresponding to every non-zero element $\gamma$ of $H^1(X,Z)$ there is either a cross section associated with $\gamma$ or one associated with $-\gamma$. We obtain necessary and sufficient conditions for this to hold; on the $(k+1)$-dimensional torus these conditions take a classical form.

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