Hyperbolic geometry, continued fractions and classification of the finitely generated totally ordered dimension groups
نویسنده
چکیده
We classify polycyclic totally ordered dimension groups, i.e. dimension groups generated by dense embeddings of the lattice Zn in the real line R . Our method is based on geometry of simple geodesics on the modular surface of genus g ≥ 2. The main theorem says that isomorphism classes of the polycyclic totally ordered dimension group are bijective with the reals α modulo the action of the group GL(2,Z). The result is an extension of the Effros-Shen classification of the dicyclic dimension groups.
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