The Farrell-Jones Isomorphism Conjecture in K-Theory

2012/02/26 by Morteo, Marcelo Gomez
#12610 #16E60 #20E08 #55N91 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1202.5759

Abstract

We prove that the Farrell-Jones isomorphism conjecture for non-connective algebraic K-theory for a discrete group G and a coefficient ring R holds true if G belongs to the class of groups acting on trees, under certain conditions on G (see theorem 0.5 below) and if the coefficient ring R is either regular or hereditary, depending on the structure of G. Our result is weaker than the result that has been established in [15] which says that these groups verify the conjecture for any coefficient ring, see remark 0.6 below.

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