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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Counterexamples on the rank of a manifold


Author: Glen E. Bredon
Journal: Proc. Amer. Math. Soc. 27 (1971), 592-594
MSC: Primary 57.34
DOI: https://doi.org/10.1090/S0002-9939-1971-0270394-0
MathSciNet review: 0270394
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Abstract: For any given integer $ r$ a closed manifold is constructed which has a smooth free action of the $ r$-torus, and hence has rank at least $ r$, but for which -1 is not a multiple root of the Poincaré polynomial.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0270394-0
Keywords: Commuting vector fields, Poincaré polynomial, free toral action
Article copyright: © Copyright 1971 American Mathematical Society