L-theory

Summary

L-theory is the K-theory of quadratic forms over a ring with involution. It assigns to such a ring $R$ abelian groups $L_n(R)$, periodic in $n$ with period $4$. Wall introduced these groups as the home of obstructions in surgery theory. Ranicki gave an algebraic theory of them through chain complexes with Poincaré duality. The L-groups of the integers are $\Z$, $0$, $\Z/2$, $0$ in degrees $0, 1, 2, 3$ modulo $4$.