Title: On the isomorphism conjecture
for groups acting on trees
Abstract: 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 so that the vertex stabilizers satisfy the
conjecture. These conditions are satisfied in some useful cases of the
conjecture. We prove some general results on the conjecture for the
pseudoisotopy theory for groups acting on trees with residually finite
stabilizers. In particular, we study situations when the vertex
stabilizers belong to the following classes of groups: polycyclic
groups, finitely generated nilpotent groups, closed
surface groups, finitely generated abelian groups and virtually cyclic
We also develop some methods which are used in later work for the conjecture in L-theory.
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