On the Isomorphism Conjecture in algebraic K-theory

2001/08/21 by Arthur Bartels, Bartels, Arthur, Tom Farrell +5
Mathematics · #19A31 #19B28 #19D35 #19D50 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #K-Theory and Homology (math.KT) #math.AT #math.GT #math.KT #msc:19A31 #msc:19B28 #msc:19D35 #msc:19D50

paper · pdf · doi:10.48550/arxiv.math/0108139

64 pages

arxiv created 2001/08/21 · arxiv updated 2009/11/30

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.

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