Whitehead groups Wh(π), where
The expression is non-unique: the manipulation of handlebody decompositions is an essential ingredient of the proof of the Smale h-cobordism theorem, and its generalization to the s-cobordism theorem.
This kind of cobordism theory is a homology theory whose coefficients have been calculated by Thom: therefore the cobordism classes of such maps are computable at least in theory for all spaces .