English

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.

Keywords

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

R2 v1 2026-07-22T16:40:03.652Z