Whitehead group

Summary

The Whitehead group $\mathrm{Wh}(G)$ of a group $G$ is a quotient of K1 of the integral group ring $\Z[G]$. One divides out the classes of the trivial units $\pm g$. It is the home of Whitehead torsion, which decides whether a homotopy equivalence of finite CW complexes is a simple homotopy equivalence. Through the s-cobordism theorem, its vanishing for $\pi_1$ is what makes h-cobordisms of high-dimensional manifolds trivial.