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714 analogous to a simplicial space (but with cone-product polyhedra replacing simplices). |
714 analogous to a simplicial space (but with cone-product polyhedra replacing simplices). |
715 More specifically, a generator of $\cB\cT_k(X)$ is an $i$-parameter family of $j$-blob diagrams, with $i+j=k$. |
715 More specifically, a generator of $\cB\cT_k(X)$ is an $i$-parameter family of $j$-blob diagrams, with $i+j=k$. |
716 |
716 |
717 With this alternate version in hand, it is straightforward to prove the theorem. |
717 With this alternate version in hand, it is straightforward to prove the theorem. |
718 The evaluation map $\Homeo(X)\times BD_j(X)\to BD_j(X)$ |
718 The evaluation map $\Homeo(X)\times BD_j(X)\to BD_j(X)$ |
719 induces a chain map $\CH{X}\ot C_*(BD_j(X))\to C_*(BD_j(X))$ |
719 induces a chain map $\CH{X}\tensor C_*(BD_j(X))\to C_*(BD_j(X))$ |
720 and hence a map $e_X: \CH{X} \ot \cB\cT_*(X) \to \cB\cT_*(X)$. |
720 and hence a map $e_X: \CH{X} \tensor \cB\cT_*(X) \to \cB\cT_*(X)$. |
721 It is easy to check that $e_X$ thus defined has the desired properties. |
721 It is easy to check that $e_X$ thus defined has the desired properties. |
722 \end{proof} |
722 \end{proof} |
723 |
723 |
724 \begin{thm} |
724 \begin{thm} |
725 \label{thm:blobs-ainfty} |
725 \label{thm:blobs-ainfty} |