# HG changeset patch # User Kevin Walker # Date 1279421866 21600 # Node ID 901a7c79976b7bedc2c1c6ddd3ffec0fb3d6a76b # Parent c3fb6e8a71366f3d093714771f0510e7743cd7fe# Parent 45807ce1561501766e105abfef97c95570a1f2af Automated merge with https://tqft.net/hg/blob/ diff -r 45807ce15615 -r 901a7c79976b diagrams/smallblobs/tent.pdf Binary file diagrams/smallblobs/tent.pdf has changed diff -r 45807ce15615 -r 901a7c79976b diagrams/tempkw/jun23b.pdf Binary file diagrams/tempkw/jun23b.pdf has changed diff -r 45807ce15615 -r 901a7c79976b diagrams/tempkw/jun23c.pdf Binary file diagrams/tempkw/jun23c.pdf has changed diff -r 45807ce15615 -r 901a7c79976b sandbox.tex --- a/sandbox.tex Sat Jul 17 20:57:35 2010 -0600 +++ b/sandbox.tex Sat Jul 17 20:57:46 2010 -0600 @@ -11,20 +11,26 @@ \title{Sandbox} \begin{document} -\begin{equation*} -\mathfig{.4}{tempkw/feb21d} -\end{equation*} - $$ -\begin{tikzpicture}[baseline,line width = 2pt] -\draw[blue] (0,0) circle (2); -\fill[red] (0,0) circle (0.1); -\foreach \qm/\qa/\n in {70/-30/0, 120/95/1, -120/180/2} { - \draw[red] (0,0) -- (\qm:2); - \path (\qa:1) node {\color{green!50!brown} $\cA_\n$}; - \path (\qm+20:2.5) node(M\n) {\color{green!50!brown} $\cM_\n$}; - \draw[line width=1pt, green!50!brown, ->] (M\n.\qm+135) to[out=\qm+135,in=\qm+90] (\qm+5:1.3); +\begin{tikzpicture}[baseline,line width = 1pt,x=1.5cm,y=1.5cm] +\draw (0,0) node(R) {} + -- (0.75,0) node[below] {$\bar{B}$} + --(1.5,0) node[circle,fill=black,inner sep=2pt] {} + arc (0:80:1.5) node[above] {$D \times I$} + arc (80:180:1.5); +\foreach \r in {0.3, 0.6, 0.9, 1.2} { + \draw[blue!50, line width = 0.5pt] (\r,0) arc (0:180:\r); } +\draw[fill=white] + (R) node[circle,fill=black,inner sep=2pt] {} + arc (45:65:3) node[below] {$B$} + arc (65:90:3) node[below] {$A$} + arc (90:135:3) node[circle,fill=black,inner sep=2pt] {} + arc (-135:-90:3) node[below] {$C$} + arc (-90:-45:3); +\draw[fill] (150:1.5) circle (2pt) node[above=4pt] {$D$}; +\node at (-2,0) {\scalebox{2.0}{$\uparrow f$}}; +\node at (0.2,0.8) {\scalebox{2.0}{$\uparrow \psi$}}; \end{tikzpicture} $$ \end{document} diff -r 45807ce15615 -r 901a7c79976b text/a_inf_blob.tex --- a/text/a_inf_blob.tex Sat Jul 17 20:57:35 2010 -0600 +++ b/text/a_inf_blob.tex Sat Jul 17 20:57:46 2010 -0600 @@ -103,7 +103,7 @@ However, we {\it can} find another decomposition $L$ such that $L$ shares common refinements with both $K$ and $K'$. Let $KL$ and $K'L$ denote these two refinements. -Then filtration degree 1 chains associated to the four anti-refinemnts +Then filtration degree 1 chains associated to the four anti-refinements $KL\to K$, $KL\to L$, $K'L\to L$ and $K'L\to K'$ give the desired chain connecting $(a, K)$ and $(a, K')$ (see Figure \ref{zzz4}). diff -r 45807ce15615 -r 901a7c79976b text/ncat.tex --- a/text/ncat.tex Sat Jul 17 20:57:35 2010 -0600 +++ b/text/ncat.tex Sat Jul 17 20:57:46 2010 -0600 @@ -2114,9 +2114,28 @@ \] (See Figure \ref{jun23b}.) \begin{figure}[t] -\begin{equation*} -\mathfig{.5}{tempkw/jun23b} -\end{equation*} +$$ +\begin{tikzpicture}[baseline,line width = 1pt,x=1.5cm,y=1.5cm] +\draw (0,0) node(R) {} + -- (0.75,0) node[below] {$\bar{B}$} + --(1.5,0) node[circle,fill=black,inner sep=2pt] {} + arc (0:80:1.5) node[above] {$D \times I$} + arc (80:180:1.5); +\foreach \r in {0.3, 0.6, 0.9, 1.2} { + \draw[blue!50, line width = 0.5pt] (\r,0) arc (0:180:\r); +} +\draw[fill=white] + (R) node[circle,fill=black,inner sep=2pt] {} + arc (45:65:3) node[below] {$B$} + arc (65:90:3) node[below] {$A$} + arc (90:135:3) node[circle,fill=black,inner sep=2pt] {} + arc (-135:-90:3) node[below] {$C$} + arc (-90:-45:3); +\draw[fill] (150:1.5) circle (2pt) node[above=4pt] {$D$}; +\node[green!50!brown] at (-2,0) {\scalebox{2.0}{$\uparrow f$}}; +\node[green!50!brown] at (0.2,0.8) {\scalebox{2.0}{$\uparrow \psi$}}; +\end{tikzpicture} +$$ \caption{Moving $B$ from top to bottom} \label{jun23b} \end{figure} @@ -2136,7 +2155,26 @@ (See Figure \ref{jun23c}.) \begin{figure}[t] \begin{equation*} -\mathfig{.5}{tempkw/jun23c} +\begin{tikzpicture}[baseline,line width = 1pt,x=1.5cm,y=-1.5cm] +\draw (0,0) node(R) {} + -- (0.75,0) node[above] {$B$} + --(1.5,0) node[circle,fill=black,inner sep=2pt] {} + arc (0:80:1.5) node[below] {$D' \times I$} + arc (80:180:1.5); +\foreach \r in {0.3, 0.6, 0.9, 1.2} { + \draw[blue!50, line width = 0.5pt] (\r,0) arc (0:180:\r); +} +\draw[fill=white] + (R) node[circle,fill=black,inner sep=2pt] {} + arc (45:65:3) node[above] {$\bar{B}$} + arc (65:90:3) node[below] {$C$} + arc (90:135:3) node[circle,fill=black,inner sep=2pt] {} + arc (-135:-90:3) node[below] {$A$} + arc (-90:-45:3); +\draw[fill] (150:1.5) circle (2pt) node[below=4pt] {$D'$}; +\node[green!50!brown] at (-2,0) {\scalebox{2.0}{$f'\uparrow $}}; +\node[green!50!brown] at (0.2,0.8) {\scalebox{2.0}{$\psi^+\uparrow $}}; +\end{tikzpicture} \end{equation*} \caption{Moving $B$ from bottom to top} \label{jun23c}