\begin{tikzpicture}[description/.style={fill=white,inner sep=2pt}] \matrix(a)[matrix of math nodes, row sep=2em, column sep=2.5em, text height=1.5ex, text depth=0.25ex] { & \pi_1(U_1)\\

 \pi_1(U_1\cap U_2) & & \pi_1(U_1) *_{\pi_1(U_1\cap U_2)} \pi_1(U_2) & & \pi_1(X)\\
& \pi_1(U_2)\\};

\path[->](a-2-1) edge node[below]{$i_2$} (a-3-2); \path[->](a-2-1) edge node[above]{$i_1$} (a-1-2); \path[->](a-1-2) edge[bend left=10] node[above]{$j_1$} (a-2-5); \path[->](a-3-2) edge[bend right=10] node[below]{$j_2$} (a-2-5); \path[->,dashed](a-2-3) edge node[description]{$k$} (a-2-5); \path[->,dashed](a-1-2) edge node[]{} (a-2-3); \path[->,dashed](a-3-2) edge node[]{} (a-2-3);