diff -r 7d7f9e7c5869 -r 3311fa1c93b9 text/ncat.tex --- a/text/ncat.tex Wed Nov 30 18:45:32 2011 -0800 +++ b/text/ncat.tex Fri Dec 02 21:42:38 2011 -0800 @@ -383,24 +383,24 @@ \begin{tikzpicture}[baseline=0] \begin{scope} \path[clip] (0,0) arc (135:45:4) arc (-45:-135:4); -\draw[blue,line width=2pt] (0,0) arc (135:45:4) arc (-45:-135:4); +\draw[kw-blue-a,line width=2pt] (0,0) arc (135:45:4) arc (-45:-135:4); \foreach \x in {0, 0.5, ..., 6} { \draw[green!50!brown] (\x,-2) -- (\x,2); } \end{scope} -\draw[blue,line width=1.5pt] (0,-3) -- (5.66,-3); +\draw[kw-blue-a,line width=1.5pt] (0,-3) -- (5.66,-3); \draw[->,red,line width=2pt] (2.83,-1.5) -- (2.83,-2.5); \end{tikzpicture} \qquad \qquad \begin{tikzpicture}[baseline=-0.15cm] \begin{scope} \path[clip] (0,1) arc (90:135:8 and 4) arc (-135:-90:8 and 4) -- cycle; -\draw[blue,line width=2pt] (0,1) arc (90:135:8 and 4) arc (-135:-90:8 and 4) -- cycle; +\draw[kw-blue-a,line width=2pt] (0,1) arc (90:135:8 and 4) arc (-135:-90:8 and 4) -- cycle; \foreach \x in {-6, -5.5, ..., 0} { \draw[green!50!brown] (\x,-2) -- (\x,2); } \end{scope} -\draw[blue,line width=1.5pt] (-5.66,-3.15) -- (0,-3.15); +\draw[kw-blue-a,line width=1.5pt] (-5.66,-3.15) -- (0,-3.15); \draw[->,red,line width=2pt] (-2.83,-1.5) -- (-2.83,-2.5); \end{tikzpicture} $$ @@ -437,8 +437,8 @@ \begin{tikzpicture}[baseline=0] \begin{scope} \path[clip] (0,0) arc (135:45:4) arc (-45:-135:4); -\draw[blue,line width=2pt] (0,0) arc (135:45:4) arc (-45:-135:4); -\draw[blue] (0,0) -- (5.66,0); +\draw[kw-blue-a,line width=2pt] (0,0) arc (135:45:4) arc (-45:-135:4); +\draw[kw-blue-a] (0,0) -- (5.66,0); \foreach \x in {0, 0.5, ..., 6} { \draw[green!50!brown] (\x,-2) -- (\x,2); } @@ -448,8 +448,8 @@ \begin{tikzpicture}[baseline=0] \begin{scope} \path[clip] (0,-1) rectangle (4,1); -\draw[blue,line width=2pt] (0,-1) rectangle (4,1); -\draw[blue] (0,0) -- (5,0); +\draw[kw-blue-a,line width=2pt] (0,-1) rectangle (4,1); +\draw[kw-blue-a] (0,0) -- (5,0); \foreach \x in {0, 0.5, ..., 6} { \draw[green!50!brown] (\x,-2) -- (\x,2); } @@ -459,8 +459,8 @@ \begin{tikzpicture}[baseline=0] \begin{scope} \path[clip] (0,0) arc (135:45:4) arc (-45:-135:4); -\draw[blue,line width=2pt] (0,0) arc (135:45:4) arc (-45:-135:4); -\draw[blue] (2.83,3) circle (3); +\draw[kw-blue-a,line width=2pt] (0,0) arc (135:45:4) arc (-45:-135:4); +\draw[kw-blue-a] (2.83,3) circle (3); \foreach \x in {0, 0.5, ..., 6} { \draw[green!50!brown] (\x,-2) -- (\x,2); } @@ -471,8 +471,8 @@ \begin{tikzpicture}[baseline=0] \begin{scope} \path[clip] (0,-1) rectangle (4,1); -\draw[blue,line width=2pt] (0,-1) rectangle (4,1); -\draw[blue] (0,-1) -- (4,1); +\draw[kw-blue-a,line width=2pt] (0,-1) rectangle (4,1); +\draw[kw-blue-a] (0,-1) -- (4,1); \foreach \x in {0, 0.5, ..., 6} { \draw[green!50!brown] (\x,-2) -- (\x,2); } @@ -482,8 +482,8 @@ \begin{tikzpicture}[baseline=0] \begin{scope} \path[clip] (0,-1) rectangle (5,1); -\draw[blue,line width=2pt] (0,-1) rectangle (5,1); -\draw[blue] (1,-1) .. controls (2,-1) and (3,1) .. (4,1); +\draw[kw-blue-a,line width=2pt] (0,-1) rectangle (5,1); +\draw[kw-blue-a] (1,-1) .. controls (2,-1) and (3,1) .. (4,1); \foreach \x in {0, 0.5, ..., 6} { \draw[green!50!brown] (\x,-2) -- (\x,2); } @@ -493,8 +493,8 @@ \begin{tikzpicture}[baseline=0] \begin{scope} \path[clip] (0,0) arc (135:45:4) arc (-45:-135:4); -\draw[blue,line width=2pt] (0,0) arc (135:45:4) arc (-45:-135:4); -\draw[blue] (2.82,-5) -- (2.83,5); +\draw[kw-blue-a,line width=2pt] (0,0) arc (135:45:4) arc (-45:-135:4); +\draw[kw-blue-a] (2.82,-5) -- (2.83,5); \foreach \x in {0, 0.5, ..., 6} { \draw[green!50!brown] (\x,-2) -- (\x,2); } @@ -632,7 +632,7 @@ \draw (1-small) circle (\srad); \foreach \theta in {90, 72, ..., -90} { - \draw[blue] (1) -- ($(1)+(\rad,0)+(\theta:\srad)$); + \draw[kw-blue-a] (1) -- ($(1)+(\rad,0)+(\theta:\srad)$); } \filldraw[fill=white] (1) circle (\rad); \foreach \n in {1,2} { @@ -645,7 +645,7 @@ \path[clip] (2) circle (\rad); \draw[clip] (2.east) circle (\srad); \foreach \y in {1, 0.86, ..., -1} { - \draw[blue] ($(2)+(-1,\y) $)-- ($(2)+(1,\y)$); + \draw[kw-blue-a] ($(2)+(-1,\y) $)-- ($(2)+(1,\y)$); } \end{scope} \end{tikzpicture} @@ -2493,7 +2493,7 @@ Another way to say this is that $(X, M)$ is homeomorphic to $B^{k-1}\times([-1,1], \{0\})$. \begin{figure}[t] -$$\tikz[baseline,line width=2pt]{\draw[blue] (-2,0)--(2,0); \fill[red] (0,0) circle (0.1);} \qquad \qquad \tikz[baseline,line width=2pt]{\draw[blue][fill=blue!30!white] (0,0) circle (2 and 1); \draw[red] (0,1)--(0,-1);}$$ +$$\tikz[baseline,line width=2pt]{\draw[kw-blue-a] (-2,0)--(2,0); \fill[red] (0,0) circle (0.1);} \qquad \qquad \tikz[baseline,line width=2pt]{\draw[kw-blue-a][fill=kw-blue-a!30!white] (0,0) circle (2 and 1); \draw[red] (0,1)--(0,-1);}$$ \caption{0-marked 1-ball and 0-marked 2-ball} \label{feb21a} \end{figure} @@ -2535,13 +2535,13 @@ These restrictions are 0-morphisms $(a, b)$ of $\cA$ and $\cB$. \begin{figure}[t] \centering -\begin{tikzpicture}[blue,line width=2pt] +\begin{tikzpicture}[kw-blue-a,line width=2pt] \draw (0,1) -- (0,-1) node[below] {$X$}; \draw (2,0) -- (4,0) node[below] {$J$}; \fill[red] (3,0) circle (0.1); -\draw[fill=blue!30!white] (6,0) node(a) {} arc (135:90:4) node(top) {} arc (90:45:4) node(b) {} arc (-45:-90:4) node(bottom) {} arc(-90:-135:4); +\draw[fill=kw-blue-a!30!white] (6,0) node(a) {} arc (135:90:4) node(top) {} arc (90:45:4) node(b) {} arc (-45:-90:4) node(bottom) {} arc(-90:-135:4); \draw[red] (top.center) -- (bottom.center); \fill (a) circle (0.1) node[left] {\color{green!50!brown} $a$}; \fill (b) circle (0.1) node[right] {\color{green!50!brown} $b$}; @@ -2563,7 +2563,7 @@ \begin{figure}[t] \centering \begin{tikzpicture}[baseline,line width = 2pt] -\draw[blue] (0,0) -- (6,0); +\draw[kw-blue-a] (0,0) -- (6,0); \foreach \x/\n in {0.5/0,1.5/1,3/2,4.5/3,5.5/4} { \path (\x,0) node[below] {\color{green!50!brown}$\cA_{\n}$}; } @@ -2574,7 +2574,7 @@ \qquad \qquad \begin{tikzpicture}[baseline,line width = 2pt] -\draw[blue] (0,0) circle (2); +\draw[kw-blue-a] (0,0) circle (2); \foreach \q/\n in {-45/0,90/1,180/2} { \path (\q:2.4) node {\color{green!50!brown}$\cA_{\n}$}; } @@ -2613,7 +2613,7 @@ \begin{figure}[t] \centering \begin{tikzpicture}[baseline,line width = 2pt] -\draw[blue][fill=blue!15!white] (0,0) circle (2); +\draw[kw-blue-a][fill=kw-blue-a!15!white] (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); @@ -2628,7 +2628,7 @@ \begin{figure}[t] \centering \begin{tikzpicture}[baseline,line width = 2pt] -\draw[blue][fill=blue!15!white] (0,0) circle (2); +\draw[kw-blue-a][fill=kw-blue-a!15!white] (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); @@ -3089,8 +3089,7 @@ \begin{figure}[t] -\todo{Verify that the tikz figure is correct, remove the hand-drawn one.} -$$\mathfig{.65}{tempkw/morita1}$$ +%$$\mathfig{.65}{tempkw/morita1}$$ $$ \begin{tikzpicture} @@ -3172,7 +3171,7 @@ to decorated circles. Figure \ref{morita-fig-2} \begin{figure}[t] -$$\mathfig{.55}{tempkw/morita2}$$ +%$$\mathfig{.55}{tempkw/morita2}$$ $$ \begin{tikzpicture} \node(L) at (0,0) {\tikz{ @@ -3258,7 +3257,7 @@ they must satisfy identities corresponding to Morse cancellations on 2-manifolds. These are illustrated in Figure \ref{morita-fig-3}. \begin{figure}[t] -$$\mathfig{.65}{tempkw/morita3}$$ +%$$\mathfig{.65}{tempkw/morita3}$$ $$ \begin{tikzpicture} \node(L) at (0,0) {\tikz{