Talk:Finitely dominated CW complexes (Ex)

The obstruction to a finitely dominated CW-complex to being homotopy equivalent to a finite complex lies in the group $\widetilde{K}_0(\Z[\pi_1(X)])$$<wikitex>; The obstruction to being homotopy equivalent to a finite complex lies in the group $\tilde{K}_0(\Z\pi_1(X))$ which is the trivial group if $\pi_1(M)$ is trivial. </wikitex>\widetilde{K}_0(\Z[\pi_1(X)])$ by the Wall's finiteness obstruction theorem. The related obstruction for such a 1-connected CW-complex lies so in $\widetilde{K}_0(\Z)$$\widetilde{K}_0(\Z)$ which is trivial.