Surgery obstruction groups

Summary

The surgery obstruction groups are the L-groups $L_n(\Z[\pi], w)$ of the integral group ring of a group $\pi$. Here the involution is twisted by an orientation character $w$. Wall showed that they contain the obstruction to turning a degree one normal map into a simple homotopy equivalence by surgery. This holds in dimensions at least $5$. They depend only on the fundamental group, the orientation character and the dimension modulo $4$. They are the algebraic part of the surgery exact sequence that classifies manifolds within a homotopy type.