Surgery of closed manifolds with dihedral fundamental group

In the paper the obstruction groups to obtaining simple homotopy equivalence by surgery from normal degree 1 maps of closed manifolds with dihedral fundamental group are computed. The cases of trivial orientation for the dihedral group and nontrivial orientation for the order 2 cyclic subgroup are considered. New results concerning the Browder–Livesey groups and natural maps of $L$-groups arising in index 2 inclusions of the cyclic group into the dihedral group are obtained.