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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    and the closed manifold subgroup    are equal in dimensions   , for any finitely-presented group    and any orientation character   . This answers a question raised in 1980.

Surgery obstructions on closed manifolds and the inertia subgroup