27 as shown in Figure \ref{delfig1}. |
27 as shown in Figure \ref{delfig1}. |
28 We can think of such a configuration as encoding a sequence of surgeries, starting at the bottommost interval |
28 We can think of such a configuration as encoding a sequence of surgeries, starting at the bottommost interval |
29 of Figure \ref{delfig1} and ending at the topmost interval. |
29 of Figure \ref{delfig1} and ending at the topmost interval. |
30 \begin{figure}[t] |
30 \begin{figure}[t] |
31 $$\mathfig{.9}{deligne/intervals}$$ |
31 $$\mathfig{.9}{deligne/intervals}$$ |
32 \caption{Little bigons, though of as encoding surgeries}\label{delfig1}\end{figure} |
32 \caption{Little bigons, thought of as encoding surgeries}\label{delfig1}\end{figure} |
33 The surgeries correspond to the $k$ bigon-shaped ``holes". |
33 The surgeries correspond to the $k$ bigon-shaped ``holes". |
34 We remove the bottom interval of each little bigon and replace it with the top interval. |
34 We remove the bottom interval of each little bigon and replace it with the top interval. |
35 To convert this topological operation to an algebraic one, we need, for each hole, an element of |
35 To convert this topological operation to an algebraic one, we need, for each hole, an element of |
36 $\hom(\bc^C_*(I_{\text{bottom}}), \bc^C_*(I_{\text{top}}))$, which is homotopy equivalent to $Hoch^*(C, C)$. |
36 $\hom(\bc^C_*(I_{\text{bottom}}), \bc^C_*(I_{\text{top}}))$, which is homotopy equivalent to $Hoch^*(C, C)$. |
37 So for each fixed configuration we have a map |
37 So for each fixed configuration we have a map |