We compute the homology of Ω(X∨Y) (the loop space of the wedge of the spaces X and Y), in terms of the homogies of ΩX and ΩY. To do this we use the fact that our problem is equivalent to the computation of the homology of the free product of two topological groups in terms of the homologies of the topological groups. We establish a multiple Kunneth formula with coefficients over a Dedekind domain, which is used to prove a Kunneth like formula involves homologies over a Dedekind domain and generalizes similar results with integral or field coefficients. Over a principal ideal domain the formula for a free product is made more specific.
Topological Group Free Product Loop Space Ideal Domain Dedekind Domain
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