text/ncat.tex
changeset 753 32e956a73f14
parent 752 84bf15233e08
child 754 2c9f09286beb
equal deleted inserted replaced
752:84bf15233e08 753:32e956a73f14
   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 $X_i\sub X$.
       
   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