Pillay's conjecture for groups definable in weakly o‐minimal non‐valuational structures

Abstract

Let G be a group definable in a weakly o-minimal non-valuational structure M. Then G/G 00 , equipped with the logic topology, is a compact Lie group, and if G has finitely satisfiable generics, then dim(G/G 00 ) = dim(G). Our main technical result is that G is a dense subgroup of a group definable in the canonical o-minimal extension of M.