text/evmap.tex
changeset 368 eb7a1ea85179
parent 359 6224e50c9311
child 385 b1da2a454ee7
equal deleted inserted replaced
360:92f0dac39ce3 368:eb7a1ea85179
   616 Similar arguments show that this homotopy from $e$ to $e'$ is well-defined
   616 Similar arguments show that this homotopy from $e$ to $e'$ is well-defined
   617 up to second order homotopy, and so on.
   617 up to second order homotopy, and so on.
   618 \end{proof}
   618 \end{proof}
   619 
   619 
   620 
   620 
       
   621 \noop{
       
   622 
       
   623 \nn{this should perhaps be a numbered remark, so we can cite it more easily}
       
   624 
       
   625 \begin{rem}
       
   626 For the proof of xxxx below we will need the following observation on the action constructed above.
       
   627 Let $b$ be a blob diagram and $p:P\times X\to X$ be a family of homeomorphisms.
       
   628 Then we may choose $e$ such that $e(p\ot b)$ is a sum of generators, each
       
   629 of which has support arbitrarily close to $p(t,|b|)$ for some $t\in P$.
       
   630 This follows from the fact that the 
       
   631 \nn{not correct, since there could also be small balls far from $|b|$}
       
   632 \end{rem}
       
   633 }
   621 
   634 
   622 \begin{prop}
   635 \begin{prop}
   623 The $CH_*(X, Y)$ actions defined above are associative.
   636 The $CH_*(X, Y)$ actions defined above are associative.
   624 That is, the following diagram commutes up to homotopy:
   637 That is, the following diagram commutes up to homotopy:
   625 \[ \xymatrix{
   638 \[ \xymatrix{