**S.K. Roushon**

TIFR

March 18, 2010

**The Isomorphism Conjecture for groups acting on trees**:
The Isomorphism conjecture of Farrell and Jones asserts that the K-theoretic (reduced projective class groups, algebraic K-groups) and the L-theoretic obstruction groups of a discrete group can be computed in terms of the virtually cyclic subgroups of the group. A `virtually cyclic' group, by definition, contains a cyclic subgroup of finite index. The Isomorphism Conjecture implies several fundamental conjectures, for example the vanishing of the Whitehead group for torsion free discrete groups, Borel conjecture, Novikov conjecture, etc.

We will study the conjecture for groups acting on trees and see under what conditions on the vertex stabilizers the conjecture can be deduced for the group.