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

Abstract

Let ℳ=〈 M, +, <, 0, S〉 be a linear o-minimal expansion of an ordered group, and G=〈 G, ⊕, e_G〉 an n-dimensional group definable in ℳ. 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.