On the Farrell-Jones Conjecture and its applications

نویسندگان

  • Arthur Bartels
  • Holger Reich
چکیده

We present the status of the Farrell-Jones Conjecture for algebraic K-theory for a group G and arbitrary coefficient rings R. We add new groups for which the conjecture is known to be true and study inheritance properties. We discuss new applications, focussing on the Bass Conjecture, the Kaplansky Conjecture and conjectures generalizing Moody’s Induction Theorem. Thus we extend the class of groups for which these conjectures are known considerably. Mathematics Subject Classification (2000). 19Dxx, 19A31,19B28

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

m at h . K T ] 2 7 O ct 2 00 5 COEFFICIENTS FOR THE FARRELL - JONES CONJECTURE

We introduce the Farrell-Jones Conjecture with coefficients in an additive category with G-action. This is a variant of the Farrell-Jones Conjecture about the algebraic Kor L-Theory of a group ring RG. It allows to treat twisted group rings and crossed product rings. The conjecture with coefficients is stronger than the original conjecture but it has better inheritance properties. Since known p...

متن کامل

Chern characters for proper equivariant homology theories and applications to K- and L-theory

We construct for an equivariant homology theory for proper equivariant CW -complexes an equivariant Chern character under certain conditions. This applies for instance to the sources of the assembly maps in the Farrell-Jones Conjecture with respect to the family F of finite subgroups and in the Baum-Connes Conjecture. Thus we get an explicit calculation of Q ⊗Z Kn(RG) and Q ⊗Z Ln(RG) for a comm...

متن کامل

The Farrell-jones Isomorphism Conjecture for Finite Co-volume Hyperbolic Actions and the Algebraic K-theory of Bianchi Groups

We prove the Farrell-Jones Isomorphism Conjecture for groups acting on complete hyperbolic manifolds with finite volume orbit space. We then apply this result to show that for any Bianchi group Γ, Wh(Γ), K̃0(ZΓ), and Ki(ZΓ) vanish for i ≤ −1.

متن کامل

The K-theoretic Farrell-jones Conjecture for Hyperbolic Groups

We prove the K-theoretic Farrell-Jones Conjecture for hyperbolic groups with (twisted) coefficients in any associative ring with unit.

متن کامل

Geodesic flow for CAT.0/–groups

In Bartels–Lück [1] we introduced the concept of transfer reducible groups with respect to a family of subgroups. This definition is somewhat technical and recalled as Definition 0.4 below. We showed that groups that are transfer reducible over the family of virtually cyclic subgroups satisfy the Farrell–Jones Conjecture with coefficients in an additive category. For further explanations about ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005