\documentclass[tikz]{standalone}

\usetikzlibrary{decorations.pathreplacing,decorations.markings}
\usetikzlibrary{patterns}

\standaloneconfig{margin=12pt}

\begin{document}

\begin{tikzpicture}

% sets up command for arrows in the middle of arcs
\tikzset{->-/.style={decoration={
  markings,
  mark=at position #1 with {\arrow{>}}},postaction={decorate}}}

%draw vertices and orbifold point
\draw[fill=black] (0,-1) circle [radius=2pt];
\draw[thick] (0.5,0) node {$\mathbf{\times}$};
\draw[thick] (-0.5,0) node {$\mathbf{\times}$};

%draw pending and exterior arcs
\draw[out=75,in=-180] (0,-1) to (0.5,0.25);
\draw[out=0,in=0, looseness = 1] (0,-1) to node[midway,left,scale=0.75,yshift=-4pt]{$\tau_2$} (0.5,0.25);
\draw[out=105,in=0] (0,-1) to (-0.5,0.25);
\draw[out=180,in=180, looseness = 1] (0,-1) to node[midway,right,yshift=-4pt,scale=0.75]{$\tau_1$} (-0.5,0.25);
\draw[in=0,out=0,looseness =1.75] (0,-1) to (0,0.6);
\draw[in=180,out=180,looseness=1.75] (0,-1) to (0,0.6);
\node[above,scale=0.6,yshift=-1pt] at (0,0.6) {$\tau_a$};

%draw gamma
\draw[orange,thick, out = 15, in = 165,->=-0.6] (-.75,-0.4) to (0.75,-0.4);

\node[] (G)at (1.5,-0.2){$=$};
\node[] (G)at (4.5,-0.2){$\bigoplus$};

\draw[fill=black] (3,-1) circle [radius=2pt];
\draw[thick] (3.5,0) node {$\mathbf{\times}$};
\draw[thick] (2.5,0) node {$\mathbf{\times}$};

\draw[out=75,in=-180] (3,-1) to (3.5,0.25);
\draw[out=0,in=0, looseness = 1] (3,-1) to node[midway,left,scale=0.75,yshift=-4pt]{$\tau_2$} (3.5,0.25);
\draw[out=105,in=0] (3,-1) to (2.5,0.25);
\draw[out=180,in=180, looseness = 1] (3,-1) to node[midway,right,yshift=-4pt,scale=0.75]{$\tau_1$} (2.5,0.25);
\draw[in=0,out=0,looseness =1.75] (3,-1) to (3,0.6);
\draw[in=180,out=180,looseness=1.75] (3,-1) to (3,0.6);
\node[above,scale=0.6,yshift=-1pt] at (3,0.6) {$\tau_a$};

\draw[orange,thick, out = 15, in = 165,->=-0.6] (5.75,-0.3) to (6.785,-0.3);

\draw[fill=black] (6,-1) circle [radius=2pt];
\draw[thick] (6.5,0) node {$\mathbf{\times}$};
\draw[thick] (5.5,0) node {$\mathbf{\times}$};

\draw[out=75,in=-180] (6,-1) to (6.5,0.25);
\draw[out=0,in=0, looseness = 1] (6,-1) to node[midway,left,yshift=-4pt,scale=0.75]{$\tau_2$} (6.5,0.25);
\draw[out=105,in=0] (6,-1) to (5.5,0.25);
\draw[out=180,in=180, looseness = 1] (6,-1) to node[midway,right,yshift=-4pt,scale=0.75]{$\tau_1$} (5.5,0.25);
\draw[in=0,out=0,looseness =1.75] (6,-1) to (6,0.6);
\draw[in=180,out=180,looseness=1.75] (6,-1) to (6,0.6);
\node[above,scale=0.6,yshift=-1pt] at (6,0.6) {$\tau_a$};

\draw[orange,thick, out = 15, in = 165,->=-0.6] (2.25,-0.3) to (3.325,-0.3);



\end{tikzpicture}

\end{document}