The Wall surgery obstruction groups have two interesting geometrically
defined subgroups, consisting of the surgery obstructions between closed
manifolds, and the inertial elements. We show that the inertia group
$I_{n+1}(\pi,w)$ and the closed manifold subgroup $C_{n+1}(\pi,w)$ are equal in
dimensions $n+1\geq 6$, for any finitely-presented group $\pi$ and any
orientation character $w\colon \pi \to \cy 2$.

We show that 4-dimensional conjugation manifolds are all obtained from
branched 2-fold coverings of knotted surfaces in Z/2-homology 4-spheres.