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An Inequality Between Numerical Homotopy Invariants
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1968
References
1.
Berstein, I. and Ganea, T., Homotopical nilpotency, Illinois J. Math. 5 (1961), 99–130.Google Scholar
2.
Gonea, T., Hilton, P. J., and Peterson, F. P., On the homotopy commutativity of loop-spaces and suspensions, Topology 1 (1962), 133–141.Google Scholar
3.
Hilton, P. J., On a generalization of nilpotency to semi-simplified complexes, Proc. London Math. Soc. (3) 10 (1960), 604–622.Google Scholar
6.
Milnor, J., The geometric realization of a semi-simplicial complex, Ann. of Math. (2) 65 1957), 357–362.Google Scholar
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