%\newcommand\localyellow{}%{yellow}
%\newcommand\localorange{orange}
%\newcommand\localgray{gray!50}
%\newcommand\localblue{blue!50}
\newcommand\pentascale{0.6} % gamma 1
\def\FigScale{0.42} % gamma 3
\tikzset{->-/.style={decoration={
  markings,
  mark=at position #1 with {\arrow{stealth}}},postaction={decorate}}}
 \newcommand\plaindisk[1]
 {
 \begin{scope}[scale=\pentascale]
 \coordinate (a) at (0,0);
\draw[] (0,0) circle (1.25cm);
\node (a) at (0,0) [opacity=0.65,fill,circle,inner sep=1.5pt] {};

\foreach \x in {-144,-72,0,72,144} {
   \begin{scope}[rotate=\x]
   \coordinate (\x) at (0,-1.25);
    \node (\x) at (0,-1.25) [opacity=0.5,fill,circle,inner sep=0.9pt] {};
   \end{scope}
}
%\draw [opacity=0.65] (-144) -- (-72) -- (0) -- (72) -- (144) -- (-144)
%(0) -- (144) (-144) -- (0);

%\draw[opacity=0.55] (a) to (-144)
%(a) to (-72)
%(a) to (0);
%\draw[opacity=0.65, out=5,in=30] (0) to  
%(-144);
%\draw[opacity=0.65, out=0,in=-80] (0) to  (144);
\end{scope}
}

 \begin{tikzpicture}
\plaindisk{}%{\localgray} %%%% gamma comp
\draw[thick,->-=.7, bend right=30] (-72) to (72); % blue
\draw (-72) node [fill,blue,circle,inner sep=1.3pt] {};
\draw (72) node [black,fill=mygreen,circle,inner sep=1.3pt] {};
\draw (-72) node [left,blue] {$i$};
\draw (72) node [right,mygreen] {$j$};
\end{tikzpicture}
\begin{tikzpicture}
%\draw (0,0) node {$+$};
%\draw (0,1) node {};
%\draw (0,-1) node {};
\end{tikzpicture}
\hskip -2mm
\begin{tikzpicture}
\plaindisk{}%{\localyellow} %%% gamma
\draw[thick,->-=.7,bend right=90] (72) to (-72); % green
\draw (72) node [black,fill=mygreen,circle,inner sep=1.3pt] {};
\draw (-72) node [blue,fill,circle,inner sep=1.3pt] {};
\draw (-72) node [left,blue] {$i$};
\draw (72) node [right,mygreen] {$j$};
\end{tikzpicture}
\quad\quad\quad
\def\MacroFigSlideBraceletsAnnulus{
\draw (0,0) circle (2cm);
%\draw[fill=gray!20] (0,0) circle (.4cm);
\node (a) at (0,0) [opacity=0.65,fill,circle,inner sep=2pt] {};

\draw (120:2cm) node [fill,blue,circle,inner sep=1.3pt] {};

\draw (-180:2cm) node [black,fill=mygreen,circle,inner sep=1.3pt] {};

\draw[] (120:2cm) node[left] {$i$};
\draw[] (-180:2cm) node[left] {$j$};
}
\begin{tikzpicture}[scale=\FigScale] % first
\MacroFigSlideBraceletsAnnulus

\draw[thick, black, rounded corners,->-=0.25] ([shift=(120:2cm)]0,0) -- ([shift = (-170:1.1cm)]0,0) 
arc (-170:120:1.1cm);

\draw[thick, black, rounded corners] ([shift=(120:1.1cm)]0,0) -- ([shift = (-180:1.5cm)]0,0) 
arc (-180:140:1.5cm);

\draw[thick, black, ->-=.7] ([shift=(140:1.5cm)]0,0) -- ([shift = (-180:2cm)]0,0);
\end{tikzpicture}
\quad
\begin{tikzpicture}[scale=\FigScale] % second
\MacroFigSlideBraceletsAnnulus

\draw[thick,black, rounded corners, ,->-=.1] ([shift=(-180:2cm)]0,0) 
-- ([shift = (-220:1.5cm)]0,0) 
-- ([shift = (-200:0.7cm)]0,0) 
arc (-200:140:0.7cm);

\draw[ thick,black, rounded corners] ([shift=(140:0.7cm)]0,0) -- ([shift = (-170:1.1cm)]0,0) 
arc (-170:120:1.1cm);

\draw[thick,black, rounded corners,->-=0.9] ([shift=(120:1.1cm)]0,0) -- ([shift = (-180:1.5cm)]0,0) arc (-180:110:1.5cm) -- ([shift = (120:2cm)]0,0);
\end{tikzpicture}