\documentclass[tikz]{standalone}

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

\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 interior arcs


%draw exterior boundaries
\draw[out=30,in=-30] (0,0) to (0,1.5);
\draw[out=150,in=-150] (0,0) to (0,1.5);

%add labels
\node[left,xshift=1pt,scale=0.75] at (-0.4,1.1) {$2$};
\node [right,xshift=-1pt,scale=0.75] at (0.4,1.1) {$a$};
\node [above below,xshift=-1pt,scale=0.75] at (0.1,0.4) {$1$};
\draw[in=0,out=45,looseness =0.9] (0,0) to (0,1.3);
\draw[in=180,out=135,looseness=0.9] (0,0) to (0,1.3);

%draw crossing arc
\draw[orange, thick,out=100,in=180,looseness = 1] (0.0) to (0,1.15);
\draw[orange, thick,out=0,in=-30,looseness = 2] (0,1.15) to (0,0.8);
\draw[orange, thick,out=150,in=275,looseness = 1] (0,0.8) to (-0.15,1.35);

%draw vertices and orbifold point
\draw[fill=black] (0,0) circle [radius=2pt];
\draw[fill=black] (0,1.5) circle [radius=2pt];
\draw[thick] (0,1) node {$\mathbf{\times}$};

\end{tikzpicture}

\end{document}