On the Isomorphism Conjecture in algebraic K-theory

Details On the Isomorphism Conjecture in algebraic K-theory On the Isomorphism Conjecture in algebraic K-theory

2001-08-21

arxiv.org/abs/math/0108139v1

Mathematics

Algebraic Topology

64 pages

Scientific paper

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.

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