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Call a simplicial group $G_{\bullet}$ free if for each $n$, the group $G_n$ is a free group.

  • How does the geometric realization of $G_{\bullet}$ look like?
  • Can its nondegenerate and degenerate simplices be described explicitly?
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Without knowing what the face and degeneration maps are, it is sort of impossible to say much, isn't it? – Mariano Suárez-Alvarez Feb 1 '13 at 6:10