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137 We will briefly sketch our original motivation for defining the blob complex. |
137 We will briefly sketch our original motivation for defining the blob complex. |
138 \nn{this is adapted from an old draft of the intro; it needs further modification |
138 \nn{this is adapted from an old draft of the intro; it needs further modification |
139 in order to better integrate it into the current intro.} |
139 in order to better integrate it into the current intro.} |
140 |
140 |
141 As a starting point, consider TQFTs constructed via fields and local relations. |
141 As a starting point, consider TQFTs constructed via fields and local relations. |
142 (See Section \ref{sec:tqftsviafields} or \cite{kw:tqft}.) |
142 (See \S\ref{sec:tqftsviafields} or \cite{kw:tqft}.) |
143 This gives a satisfactory treatment for semisimple TQFTs |
143 This gives a satisfactory treatment for semisimple TQFTs |
144 (i.e.\ TQFTs for which the cylinder 1-category associated to an |
144 (i.e.\ TQFTs for which the cylinder 1-category associated to an |
145 $n{-}1$-manifold $Y$ is semisimple for all $Y$). |
145 $n{-}1$-manifold $Y$ is semisimple for all $Y$). |
146 |
146 |
147 For non-semi-simple TQFTs, this approach is less satisfactory. |
147 For non-semi-simple TQFTs, this approach is less satisfactory. |