# Surgery obstructions on closed manifolds and the inertia subgroup Academic Article

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### abstract

• 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 $w\colon \pi \to \cy 2$.

### publication date

• January 1, 2012