diff -r 5234b7329042 -r 75f5c197a0d4 text/definitions.tex --- a/text/definitions.tex Sun Nov 01 20:29:33 2009 +0000 +++ b/text/definitions.tex Sun Nov 01 20:29:41 2009 +0000 @@ -27,8 +27,6 @@ is a collection of functors $\cC_k : \cM_k \to \Set$ for $0 \leq k \leq n$ together with some additional data and satisfying some additional conditions, all specified below. -\nn{refer somewhere to my TQFT notes \cite{kw:tqft}} - Before finishing the definition of fields, we give two motivating examples (actually, families of examples) of systems of fields. @@ -390,7 +388,7 @@ \end{itemize} (See Figure \ref{blob1diagram}.) \begin{figure}[!ht]\begin{equation*} -\mathfig{.9}{tempkw/blob1diagram} +\mathfig{.9}{definition/single-blob} \end{equation*}\caption{A 1-blob diagram.}\label{blob1diagram}\end{figure} In order to get the linear structure correct, we (officially) define \[ @@ -423,11 +421,11 @@ \item A pair of closed balls (blobs) $B_0, B_1 \sub X$ with disjoint interiors. \item A field $r \in \cC(X \setmin (B_0 \cup B_1); c_0, c_1)$ (where $c_i \in \cC(\bd B_i)$). -\item Local relation fields $u_i \in U(B_i; c_i)$, $i=1,2$. +\item Local relation fields $u_i \in U(B_i; c_i)$, $i=1,2$. \nn{We're inconsistent with the indexes -- are they 0,1 or 1,2? I'd prefer 1,2.} \end{itemize} (See Figure \ref{blob2ddiagram}.) \begin{figure}[!ht]\begin{equation*} -\mathfig{.9}{tempkw/blob2ddiagram} +\mathfig{.9}{definition/disjoint-blobs} \end{equation*}\caption{A disjoint 2-blob diagram.}\label{blob2ddiagram}\end{figure} We also identify $(B_0, B_1, u_0, u_1, r)$ with $-(B_1, B_0, u_1, u_0, r)$; reversing the order of the blobs changes the sign. @@ -447,7 +445,7 @@ \end{itemize} (See Figure \ref{blob2ndiagram}.) \begin{figure}[!ht]\begin{equation*} -\mathfig{.9}{tempkw/blob2ndiagram} +\mathfig{.9}{definition/nested-blobs} \end{equation*}\caption{A nested 2-blob diagram.}\label{blob2ndiagram}\end{figure} Let $r = r_1 \bullet r'$, where $r_1 \in \cC(B_1 \setmin B_0; c_0, c_1)$ (for some $c_1 \in \cC(B_1)$) and