Arrangements of symmetric products of spaces

Details Arrangements of symmetric products of spaces Arrangements of symmetric products of spaces

2003-06-27

arxiv.org/abs/math/0306399v2

Mathematics

Combinatorics

This is an updated version of the paper. In this version some results (Proposition 1.7., Theorem 1.8, Theorem 1.9, Theorem 1.1

Scientific paper

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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