O. Introduction and statement of main results 1. Horocyclic coordinates 2. The zw = t plumbing construction 3. The plumbing construction for an admissible graph 4. Deformation (TeichmiiUer) and moduli (Riemann) spaces 5. Torsion free terminal b-groups 6. One-dimensional deformation spaces 7. Deformation spaces for torsion free terminal b-groups 8. One-dimensional moduli spaces 9. Moduli spaces ...

In the present note, we discuss certain observations made by the author in February 2009 concerning strongly torsion-free profinite groups [cf. [Mzk2], Definition 1.1, (iii)]. These observations grew out of e-mail correspondences between the author, Akio Tamagawa, and Marco Boggi, as well as oral discussions between the author and Akio Tamagawa. Definition 1. Let G be a profinite group. (i) We ...

In the discussion of A-solvable groups, the question arises if a torsion-free abelian group A of finite rank is flat as a module over its endomorphism ring if every A-generated subgroup of a torsion-free A-solvable group is A-solvable. This paper gives a negative answer by constructing a torsion-free group of rank 3 for which all A-generated torsion-free groups are A-solvable, although A is not...

O. Introduction and statement of main results 1. Horocyclic coordinates 2. The zw = t plumbing construction 3. The plumbing construction for an admissible graph 4. Deformation (TeichmiiUer) and moduli (Riemann) spaces 5. Torsion free terminal b-groups 6. One-dimensional deformation spaces 7. Deformation spaces for torsion free terminal b-groups 8. One-dimensional moduli spaces 9. Moduli spaces ...

Greg Hjorth and Simon Thomas proved that the classification problem for torsion-free abelian groups of finite rank strictly increases in complexity with the rank. Subsequently, Thomas proved that the complexity of the classification problems for p-local torsion-free abelian groups of fixed rank n are pairwise incomparable as p varies. We prove that if 3 ≤ m < n and p, q are distinct primes, the...