A Künneth formula for coproducts of simplicial groups

Katz, Elyahu

doi:10.1090/S0002-9939-1976-0445502-3

A Künneth formula for coproducts of simplicial groups
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by Elyahu Katz PDF

Proc. Amer. Math. Soc. 61 (1976), 117-121 Request permission

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.

References

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The construction

4

Allan Clark and Larry Smith, The rational homotopy of a wedge, Pacific J. Math. 24 (1968), 241–246. MR 222895, DOI 10.2140/pjm.1968.24.241