On the K- and L-theory of hyperbolic and virtually finitely generated abelian groups

On the K- and L-theory of hyperbolic and virtually finitely generated abelian groups

We investigate the algebraic Kand L-theory of the group ring RG, where G is a hyperbolic or virtually finitely generated abelian group and R is an associative ring with unit.

Finitely Generated Abelian Groups

Hyperelementary Induction for K-theory of Virtually Abelian Groups

Controlled K-theory is used to show that algebraic K-theory of virtually abelian groups is described by an assembly map defined using possibly-infinite hyperelementary subgroups. The Farrell-Jones summand (coming from infinite subgroups) is parameterized by the rational projective space of the group.

Hyperelementary Assembly for K-theory of Virtually Abelian Groups

Controlled K-theory is used to show that algebraic K-theory of virtually abelian groups is described by an assembly map defined using possibly-infinite hyperelementary subgroups. The part coming from infinite subgroups is called the Farrell-Jones summand. This is shown to split from the finite-isotropy part; is parameterized by the rational projective space of the group; and a reduced version i...

MATH 436 Notes: Finitely generated Abelian groups

Definition 1.1 (Direct Products). Let {Gα}α∈I be a collection of groups indexed by an index set I. We may form the Cartesian product ∏ α∈I Gα. The elements of this Cartesian product can be denoted by tuples (aα)α∈I . We refer to the entry aα as the αth component of this tuple. We define a multiplication on this Cartesian product componentwise, i.e., (aα) ⋆ (bα) = (aα ⋆α bα) where ⋆α is the grou...