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527 Note that $X_1$ and $X_2$ can be identified with subsets of $X$, |
527 Note that $X_1$ and $X_2$ can be identified with subsets of $X$, |
528 but $X_1 \cap X_2$ might not be codimension 1, and indeed we might have $X_1 = X_2 = X$. |
528 but $X_1 \cap X_2$ might not be codimension 1, and indeed we might have $X_1 = X_2 = X$. |
529 We assume that there is a decomposition of $X$ into balls which is compatible with |
529 We assume that there is a decomposition of $X$ into balls which is compatible with |
530 $X_1$ and $X_2$. |
530 $X_1$ and $X_2$. |
531 Let $a\in \cC(X)$, and let $a_i$ denote the restriction of $a$ to $X_i\sub X$. |
531 Let $a\in \cC(X)$, and let $a_i$ denote the restriction of $a$ to $X_i\sub X$. |
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532 (We assume that $a$ is splittable with respect to the above decomposition of $X$ into balls.) |
532 Then |
533 Then |
533 \[ |
534 \[ |
534 \pi^*(a) = \pi_1^*(a_1)\bullet \pi_2^*(a_2) . |
535 \pi^*(a) = \pi_1^*(a_1)\bullet \pi_2^*(a_2) . |
535 \] |
536 \] |
536 \item |
537 \item |