  We define and study a simplicial complex which is a homogeneous space for the
group $PGL(2, K)$ over a two-dimensional local field $K$. The complex is a
generalization of the tree studied by F. Bruhat, J. Tits, J.-P. Serre and P.
Cartier in the 60's and early 70's. Such complex can be canonically attached to
the triples $x \in C \subset X$ where $X$ is an algebraic surface, $C$ is an
irreducible curve and $x$ is a smooth point on $C$ and $X$. This construction
can be used for a description of the isomorphism set of vector bundles on $X$.
