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135 $X$ is decomposable along the union of the boundaries of the blobs. |
135 $X$ is decomposable along the union of the boundaries of the blobs. |
136 \nn{need to say more here. we want to be able to glue blob diagrams, but avoid pathological |
136 \nn{need to say more here. we want to be able to glue blob diagrams, but avoid pathological |
137 behavior} |
137 behavior} |
138 \nn{need to allow the case where $B\to X$ is not an embedding |
138 \nn{need to allow the case where $B\to X$ is not an embedding |
139 on $\bd B$. this is because any blob diagram on $X_{cut}$ should give rise to one on $X_{gl}$ |
139 on $\bd B$. this is because any blob diagram on $X_{cut}$ should give rise to one on $X_{gl}$ |
140 and blobs are allowed to meet $\bd X$.} |
140 and blobs are allowed to meet $\bd X$. |
|
141 Also, the complement of the blobs (and regions between nested blobs) might not be manifolds.} |
141 |
142 |
142 Now for the general case. |
143 Now for the general case. |
143 A $k$-blob diagram consists of |
144 A $k$-blob diagram consists of |
144 \begin{itemize} |
145 \begin{itemize} |
145 \item A collection of blobs $B_i \sub X$, $i = 1, \ldots, k$. |
146 \item A collection of blobs $B_i \sub X$, $i = 1, \ldots, k$. |