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Arrangements of symmetric products of spaces

Pavle Blagojevic·Vladimir Grujic·Rade Zivaljevic
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Abstract

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 $D + SP^{n-d}(X)$ in symmetric products $SP^n(X)$ where $D\in SP^d(X)$. As an application we include a computation of the homology of the homotopy end space of the open manifold $SP^n(M_{g,k})$, where $M_{g,k}$ 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.

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Pavle Blagojevic, Vladimir Grujic, Rade Zivaljevic. 2004-09-26. Arrangements of symmetric products of spaces. https://arxiv.org/abs/math/0306399

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