Groups definable in linear o-minimal structures: the non-compact case

Abstract

AbstractLet = ⟨M, +, <, 0, S⟩ be a linear o-minimal expansion of an ordered group, and G = ⟨G, ⊕,eG) an n-dimensional group definable in . We show that if G is definably connected with respect to the t-topology, then it is definably isomorphic to a definable quotient group U/L. for some convex ∨-definable subgroup U of ⟨Mn, +⟩ and a lattice L of rank equal to the dimension of the ‘compact part’ of G.