451 research outputs found
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 K- or 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 proofs using controlled algebra carry over to the set-up with
coefficients we obtain new results about the original Farrell-Jones Conjecture.
The conjecture with coefficients implies the fibered version of the
Farrell-Jones Conjecture.Comment: 21 page
Isomorphism Conjecture for homotopy K-theory and groups acting on trees
We discuss an analogon to the Farrell-Jones Conjecture for homotopy algebraic
K-theory. In particular, we prove that if a group G acts on a tree and all
isotropy groups satisfy this conjecture, then G satisfies this conjecture. This
result can be used to get rational injectivity results for the assembly map in
the Farrell-Jones Conjecture in algebraic K-theory.Comment: 40 pages, to appear in J. Pure Applied Algebr
- …