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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Manifolds on which only tori can act


Authors: Kyung Bai Lee and Frank Raymond
Journal: Trans. Amer. Math. Soc. 304 (1987), 487-499
MSC: Primary 57S10; Secondary 57S25
DOI: https://doi.org/10.1090/S0002-9947-1987-0911081-9
MathSciNet review: 911081
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Abstract: A list of various types of connected, closed oriented manifolds are given. Each of the manifolds support some of the well-known compact transformation group properties enjoyed by aspherical manifolds. We list and describe these classes and their transformation group properties in increasing generality. We show by various examples that these implications can never be reversed. This establishes a hierarchy in terms of spaces in one direction and the properties they enjoy in the opposite direction.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0911081-9
Keywords: Compact transformation group, aspherical manifold, covering space, ends, $ K$-manifold, $ K(\pi ,\,1)$, essential manifold, admissible, injective action, inner action, compact Lie group, hyperaspherical manifold, lens space, spherical space form, toral action
Article copyright: © Copyright 1987 American Mathematical Society