14 

    14 \begin{equation*}

    15 \mathfig{.6}{tempkw/left-marked-antirefinements}

    15 \mathfig{.4}{tempkw/feb21d}

    16 

    16 \end{equation*}

    19 \begin{tikzpicture}

    19 \begin{tikzpicture}[baseline,line width = 2pt]

    20 \fill (0,0) circle (.1);

    20 \draw[blue] (0,0) circle (2);

    21 \draw (0,0) -- (2,0);

    21 \fill[red] (0,0) circle (0.1);

    22 \draw (1,0.1) -- (1,-0.1);

    22 \foreach \qm/\qa/\n in {70/-30/0, 120/95/1, -120/180/2} {

    23 

    23 	\draw[red] (0,0) -- (\qm:2);

    24 \draw [->,red] (1,0.25) -- (1,0.75);

    24 	\path (\qa:1) node {\color{green!50!brown} $\cA_\n$};

    25 

    25 	\path (\qm+20:2.5) node(M\n) {\color{green!50!brown} $\cM_\n$};

    26 \fill (0,1) circle (.1);

    26 	\draw[line width=1pt, green!50!brown, ->] (M\n.\qm+135) to[out=\qm+135,in=\qm+90] (\qm+5:1.3);

    27 \draw (0,1) -- (2,1);

    28 \end{tikzpicture}

    29 \qquad

    30 \begin{tikzpicture}

    31 \fill (0,0) circle (.1);

    32 \draw (0,0) -- (2,0);

    33 \draw (1,0.1) -- (1,-0.1);

    34 

    35 \draw [->,red] (1,0.25) -- (1,0.75);

    36 

    37 \fill (0,1) circle (.1);

    38 \draw (0,1) -- (1,1);

    39 \end{tikzpicture}

    40 \qquad

    41 \begin{tikzpicture}

    42 \fill (0,0) circle (.1);

    43 \draw (0,0) -- (3,0);

    44 \foreach \x in {0.5, 1.0, 1.25, 1.5, 2.0, 2.5} {

    45 	\draw (\x,0.1) -- (\x,-0.1);