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

 

Diffeomorphisms without periodic points


Author: J. F. Plante
Journal: Proc. Amer. Math. Soc. 88 (1983), 716-718
MSC: Primary 58F20; Secondary 57R30, 57S99
MathSciNet review: 702306
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Abstract: It is proved that a compact smooth manifold admits a selfdiffeomorphism without periodic points if and only if its Euler characteristic is zero. When the manifold has dimension $ \ne 3$ it is shown that such a diffeomorphism exists which is also volume preserving. The proof of this latter result uses a result of Gromov concerning the existence of nonsingular divergence-free vector fields, so an alternate proof of Gromov's result is sketched.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0702306-5
PII: S 0002-9939(1983)0702306-5
Keywords: Diffeomorphism, volume preserving, periodic point, vector field, divergence-free, homotopy
Article copyright: © Copyright 1983 American Mathematical Society