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41 |
41 |
42 We want the vector space $\bc_1(X)$ to capture |
42 We want the vector space $\bc_1(X)$ to capture |
43 ``the space of all local relations that can be imposed on $\bc_0(X)$". |
43 ``the space of all local relations that can be imposed on $\bc_0(X)$". |
44 Thus we say a $1$-blob diagram consists of: |
44 Thus we say a $1$-blob diagram consists of: |
45 \begin{itemize} |
45 \begin{itemize} |
46 \item An closed ball in $X$ (``blob") $B \sub X$. |
46 \item A closed ball in $X$ (``blob") $B \sub X$. |
47 \item A boundary condition $c \in \cF(\bdy B) = \cF(\bd(X \setmin B))$. |
47 \item A boundary condition $c \in \cF(\bdy B) = \cF(\bd(X \setmin B))$. |
48 \item A field $r \in \cF(X \setmin B; c)$. |
48 \item A field $r \in \cF(X \setmin B; c)$. |
49 \item A local relation field $u \in U(B; c)$. |
49 \item A local relation field $u \in U(B; c)$. |
50 \end{itemize} |
50 \end{itemize} |
51 (See Figure \ref{blob1diagram}.) Since $c$ is implicitly determined by $u$ or $r$, we usually omit it from the notation. |
51 (See Figure \ref{blob1diagram}.) Since $c$ is implicitly determined by $u$ or $r$, we usually omit it from the notation. |