  In 1983 Culler and Shalen established a way to construct essential surfaces
in a 3-manifold from ideal points of the $SL_2$-character variety associated to
the 3-manifold group. We present in this article an analogous construction of
certain kinds of branched surfaces (which we call essential tribranched
surfaces) from ideal points of the $SL_n$-character variety for a natural
number $n$ greater than or equal to 3. Further we verify that such a branched
surface induces a nontrivial presentation of the 3-manifold group in terms of
the fundamental group of a certain 2-dimensional complex of groups.
