On topological split Kac-Moody groups and their twin buildings

Abstract

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 Muhlherr, 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.