Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2006, January 4.

Abstract:
Let M=(M, +, <, 0) be an ordered vector space over an ordered division ring D, and G an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to t-topology, then it is definably isomorphic to a `definable quotient group' U/L, for some convex V-definable subgroup U of (M^n, +) and a lattice L of rank n. As two consequences, we derive Pillay's conjecture for M as above and we show that the o-minimal fundamental group of G is isomorphic to L.

Mathematics Subject Classification (2000): 03C64, 22C05, 46A40.

Keywords and Phrases: O-minimal structures, Definably compact groups, Quotient by lattice.

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