On the rank of a space

Allday, Christopher

doi:10.1090/S0002-9947-1972-0292071-8

On the rank of a space
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by Christopher Allday PDF

Trans. Amer. Math. Soc. 166 (1972), 173-185 Request permission

Abstract:

The rank of a space is defined as the dimension of the highest dimensional torus which can act almost-freely on the space. (By an almost-free action is meant one for which all the isotropy subgroups are finite.) This definition is shown to extend the classical definition of the rank of a Lie group. A conjecture giving an upper bound for the rank of a space in terms of its rational homotopy is investigated.

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