Nilpotent class field theory for manifolds

Three-manifolds Class Field Theory (homology of Coverings for a Non-virtually Haken Manifold)

Introduction 2 1. Preliminary results in group cohomology 4 2. Free Zp-action in three-manifolds 7 3. Free Zp⊕Zp-action in three-manifolds 8 4. Algebraic study of linking forms 12 5. Linking forms and transfer nonvanishing theorem 13 6. The structure of anisotropic extensions, I 14 7. Shrinking 16 8. Isotropic extension 17 9. Blowing upH1: the non-abelian step 18 10. Class towers and the struct...

Counting Manifolds and Class Field Towers

In [BGLM] and [GLNP] it was conjectured that if H is a simple Lie group of real rank at least 2, then the number of conjugacy classes of (arithmetic) lattices in H of covolume at most x is x log x/ log log x where γ(H) is an explicit constant computable from the (absolute) root system of H . In this paper we prove that this conjecture is false. In fact, we show that the growth is at rate x log ...

Class Field Theory

Class Field Theory

Computational class field theory

Class field theory furnishes an intrinsic description of the abelian extensions of a number field which is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such extensions.