658 	(for fixed restrictions to the boundaries of the pieces),

   658 	(for fixed restrictions to the boundaries of the pieces),

   659 	\item the $s_i$'s corresponding to innermost blobs evaluate to zero in $\cC$, and

   659 	\item the $s_i$'s corresponding to innermost blobs evaluate to zero in $\cC$, and

   660 	\item the $s_i$'s corresponding to the other pieces are single fields (linear combinations with only one term).

   660 	\item the $s_i$'s corresponding to the other pieces are single fields (linear combinations with only one term).

   661 \end{itemize}

   661 \end{itemize}

   662 %that for any innermost blob $B$, the field on $B$ goes to zero under the gluing map from $\cC$. 

   662 %that for any innermost blob $B$, the field on $B$ goes to zero under the gluing map from $\cC$. 

   664 We call such linear combinations which evaluate to zero on a blob $B$ a ``null field on $B$".

   663 We call such linear combinations which evaluate to zero on a blob $B$ a ``null field on $B$".

   665 

   665 

   666 The differential acts on a $k$-blob diagram by summing over ways to forget one of the $k$ blobs, with alternating signs.

   666 The differential acts on a $k$-blob diagram by summing over ways to forget one of the $k$ blobs, with alternating signs.

   667 

   667 

   668 We now spell this out for some small values of $k$. 

   668 We now spell this out for some small values of $k$. 

   669 For $k=0$, the $0$-blob group is simply linear combinations of fields (string diagrams) on $W$. 

   669 For $k=0$, the $0$-blob group is simply linear combinations of fields (string diagrams) on $W$.