On the Isomorphism Conjecture in algebraic K-theory
Algebraic Topology
2007-05-23 v1 Geometric Topology
K-Theory and Homology
Abstract
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.
Cite
@article{arxiv.math/0108139,
title = {On the Isomorphism Conjecture in algebraic K-theory},
author = {Arthur Bartels and Tom Farrell and Lowell Jones and Holger Reich},
journal= {arXiv preprint arXiv:math/0108139},
year = {2007}
}
Comments
64 pages