On the isomorphism conjecture for groups acting on trees

Details On the isomorphism conjecture for groups acting on trees On the isomorphism conjecture for groups acting on trees

2005-10-14

arxiv.org/abs/math/0510297v5

Mathematics

K-Theory and Homology

32 pages, amslatex file. Updated and improved version. Notations are simplified. Also some errors are corrected. Several class

Scientific paper

We study the Fibered Isomorphism conjecture of Farrell and Jones for groups acting on trees. We show that under certain conditions the conjecture is true for groups acting on trees when the stabilizers satisfy the conjecture. These conditions are satisfied in several cases of the conjecture. We prove some general results on the conjecture for the pseudoisotopy theory for groups acting on trees with residually finite vertex stabilizers. In particular, we study situations when the stabilizers belong to the following classes of groups: polycyclic groups, finitely generated nilpotent groups, closed surface groups, finitely generated abelian groups and virtually cyclic groups. Finally, we provide explicit examples of groups for which we have proved the conjecture in this article and show that these groups were not considered before. Furthermore, we deduce that these groups are neither hyperbolic nor CAT(0).

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