Homotopy Groups of Diagonal Complements

  title={Homotopy Groups of Diagonal Complements},
  author={Sadok Kallel and In{\`e}s Saihi},
  journal={arXiv: Algebraic Topology},
For $X$ a connected finite simplicial complex we consider $\Delta^d(X,n)$ the space of configurations of $n$ ordered points of $X$ such that no $d+1$ of them are equal, and $B^d(X,n)$ the analogous space of configurations of unordered points. These reduce to the standard configuration spaces of distinct points when $d=1$. We describe the homotopy groups of $\Delta^d(X,n)$ (resp. $B^d(X,n)$) in terms of the homotopy (resp. homology) groups of $X$ through a range which is generally sharp. It is… Expand

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