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

====Comments====

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  G. de Rham,   "Torsion et type simple d'homotopie" , ''Lect. notes in math.'' , '''48''' , Springer  (1967)</TD></TR></table>