On the Isomorphism Conjecture in algebraic K-theory, by Arthur Bartels, Tom Farrell, Lowell Jones, and Holger Reich

The Isomorphism Conjecture is a conceptional approach towards a calculation of the algebraic K-theory of a group ring RG, where G is an infinite group. In this paper we prove the conjecture in dimensions n<2 for fundamental groups of closed Riemannian manifolds with strictly negative sectional curvature and an arbitrary coefficient ring R. If R is regular this leads to a concrete calculation of low dimensional K-theory groups of RG in terms of the K-theory of R and the homology of the group.

Arthur Bartels <bartelsa@math.uni-muenster.de>
Tom Farrell <farrell@math.binghamton.edu>
Lowell Jones <lejones@math.sunysb.edu>
Holger Reich <reichh@math.uni-muenster.de>