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An Inequality Between Numerical Homotopy Invariants

Published online by Cambridge University Press:  20 November 2018

M. J. M. Priddis
M. J. M. Priddis*
Affiliation:
Birmingham University, Birmingham, England; Liverpool University, Liverpool, England
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In (1), Berstein and Ganea denned the nilpotency class of a based topological space. For a based topological space X we write nil X for the nilpotency class of the group ΩX in the category of based topological spaces and based homotopy classes. Hilton, in (3), defined the nilpotency class, nil class K of a based semi-simplicial (s.-s.) complex; actually, the restriction of connectedness can be removed. Hence, by using the total singular complex functor S, an invariant (nil class SX) can be defined for a based topological space X.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1295 - 1299
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Berstein, I. and Ganea, T., Homotopical nilpotency, Illinois J. Math. 5 (1961), 99–130.Google Scholar
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