equal
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inserted
replaced
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 $\cC$. |
663 \nn{yech} |
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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 $B$". |
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664 % could maybe say something here like "if blobs have nice complements then this is just...." |
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 $W$. |