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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A Künneth formula for coproducts of simplicial groups


Author: Elyahu Katz
Journal: Proc. Amer. Math. Soc. 61 (1976), 117-121
MSC: Primary 55J25; Secondary 18G15, 57F99
DOI: https://doi.org/10.1090/S0002-9939-1976-0445502-3
MathSciNet review: 0445502
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Abstract: Berstein [1] (and later Clark and Smith [9]) proved that over a field the homology of the coproduct of two simplicial groups is isomorphic to the coproduct of the augmented algebras obtained by taking the homology of these groups. It turns out that this result does not hold in general over the integers. However, we obtain a Kunneth like formula in which the homology of the coproduct of two groups is expressed in terms of the homology of the groups.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0445502-3
Keywords: Coproduct of simplicial groups, coproduct of differential graded algebras, acyclic models
Article copyright: © Copyright 1976 American Mathematical Society