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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the rank of a space


Author: Christopher Allday
Journal: Trans. Amer. Math. Soc. 166 (1972), 173-185
MSC: Primary 55C10
MathSciNet review: 0292071
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0292071-8
PII: S 0002-9947(1972)0292071-8
Keywords: Rank, torus group, Borel setting, rational homotopy, Postnikov resolution
Article copyright: © Copyright 1972 American Mathematical Society