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 groups.

We also develop some methods which are used in later work for the conjecture in L-theory

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