158 Let $R_i = B\setmin \pi(D_i)$.

   158 Let $R_i = B\setmin \pi(D_i)$.

   159 Let $f_i = \rm{id}$ for all $i$.

   159 Let $f_i = \rm{id}$ for all $i$.

   160 We have now defined a map from the little $n{+}1$-balls operad to the $n$-SC operad,

   160 We have now defined a map from the little $n{+}1$-balls operad to the $n$-SC operad,

   161 with contractible fibers.

   161 with contractible fibers.

   162 (The fibers correspond to moving the $D_i$'s in the $x_{n+1}$ 

   162 (The fibers correspond to moving the $D_i$'s in the $x_{n+1}$ 

   164 %\nn{issue: we've described this by varying the $R_i$'s, but above we emphasize varying the $f_i$'s.

   164 %\nn{issue: we've described this by varying the $R_i$'s, but above we emphasize varying the $f_i$'s.

   165 %does this need more explanation?}

   165 %does this need more explanation?}

   166 

   166 

   167 Another familiar subspace of the $n$-SC operad is $\Homeo(M_0\to N_0)$, which corresponds to 

   167 Another familiar subspace of the $n$-SC operad is $\Homeo(M_0\to N_0)$, which corresponds to 

   168 case $k=0$ (no holes).

   168 case $k=0$ (no holes).