Manifolds on which only tori can act

Lee, Kyung Bai; Raymond, Frank

doi:10.1090/S0002-9947-1987-0911081-9

Manifolds on which only tori can act
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Trans. Amer. Math. Soc. 304 (1987), 487-499 Request permission

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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Injective actions of toral groups

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