We prove that a two-spherical split Kac–Moody group over a local field naturally
provides a topological twin building in the sense of Kramer. This existence result and
the local-to-global principle for twin building topologies combined with the theory of
Moufang foundations as introduced and studied by Mühlherr, Ronan, and Tits
allows one to immediately obtain a classification of two-spherical split Moufang
topological twin buildings whose underlying Coxeter diagram contains no loop and no
isolated vertices. we obtain a similar classification for split Moufang topological twin
buildings.
