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592 Note in particular that when $k=1$ this implies a $C_*(\Homeo(I))$ action on $A$. |
592 Note in particular that when $k=1$ this implies a $C_*(\Homeo(I))$ action on $A$. |
593 (Compare with Example \ref{ex:e-n-alg} and the discussion which precedes it.) |
593 (Compare with Example \ref{ex:e-n-alg} and the discussion which precedes it.) |
594 Given a non-standard interval $J$, we define $\cC(J)$ to be |
594 Given a non-standard interval $J$, we define $\cC(J)$ to be |
595 $(\Homeo(I\to J) \times A)/\Homeo(I\to I)$, |
595 $(\Homeo(I\to J) \times A)/\Homeo(I\to I)$, |
596 where $\beta \in \Homeo(I\to I)$ acts via $(f, a) \mapsto (f\circ \beta\inv, \beta_*(a))$. |
596 where $\beta \in \Homeo(I\to I)$ acts via $(f, a) \mapsto (f\circ \beta\inv, \beta_*(a))$. |
597 \nn{check this} |
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598 Note that $\cC(J) \cong A$ (non-canonically) for all intervals $J$. |
597 Note that $\cC(J) \cong A$ (non-canonically) for all intervals $J$. |
599 We define a $\Homeo(J)$ action on $\cC(J)$ via $g_*(f, a) = (g\circ f, a)$. |
598 We define a $\Homeo(J)$ action on $\cC(J)$ via $g_*(f, a) = (g\circ f, a)$. |
600 The $C_*(\Homeo(J))$ action is defined similarly. |
599 The $C_*(\Homeo(J))$ action is defined similarly. |
601 |
600 |
602 Let $J_1$ and $J_2$ be intervals. |
601 Let $J_1$ and $J_2$ be intervals. |