Arrangements of symmetric products of spaces

الأصل · EN

Using the topological technique of diagrams of spaces, we calculate the homology of the union and the complement of finite arrangements of subspaces of the form D + SPⁿ⁻ᵈ(X) in symmetric products SPⁿ(X) where D∈ SPᵈ(X). As an application we include a computation of the homology of the homotopy end space of the open manifold SPⁿ(Mg,ₖ), where Mg,ₖ is a Riemann surface of genus g punctured at k points, a problem which was originally motivated by the study of commutative (m+k,m)-groups.