if "m" and "n" are not assumed to be simply connected, then an "h"-cobordism need not be a cylinder. the "s"-cobordism theorem, due independently to mazur, stallings, and barden, explains the general situation: an "h"-cobordism is a cylinder if and only if the whitehead torsion of the inclusion vanishes. this generalizes the "h"-cobordism theorem because the simple connectedness hypotheses imply that the relevant whitehead group is trivial. in fact the "s"-cobordism theorem implies that there is a bijective correspondence between isomorphism classes of "h"-cobordisms and elements of the whitehead group.