Simple homotopy type

Two CW-complexes $ K $, $ L $ are simple homotopy equivalent if there is a homotopy equivalence $ \tau : K \rightarrow L $ whose Whitehead torsion vanishes. An equivalence class under simple homotopy equivalence is called a simple homotopy type.

References

[a1]	G. de Rham, "Torsion et type simple d'homotopie" , Lect. notes in math. , 48 , Springer (1967)