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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Poincaré flows


Author: Sol Schwartzman
Journal: Proc. Amer. Math. Soc. 125 (1997), 2493-2500
MSC (1991): Primary 58F25
MathSciNet review: 1415369
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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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Additional Information

Sol Schwartzman
Affiliation: Department of Mathematics, University of Rhode Island, Kingston, Rhode Island 02881-0806

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04032-X
PII: S 0002-9939(97)04032-X
Received by editor(s): February 26, 1996
Communicated by: Linda Keen
Article copyright: © Copyright 1997 American Mathematical Society