2026/07/16 by Thang Nguyen, Theodore Weisman
#math.DS #math.GR #math.MG
When X is a locally compact Euclidean building, the isometry group of X acts by homeomorphisms on the space of k-simplices in the visual boundary of X. We consider perturbations of these actions for discrete groups of isometries acting with compact quotient on X, showing that all small enough perturbations are semi-conjugate to the original action. This proves in particular that, when Q is any parabolic subgroup in a semisimple p-adic Lie group G, the induced action of a cocompact lattice in G has a topologically stable action on G/Q.