an obvious question associated with the existence of "h"-cobordisms is their uniqueness. the natural notion of equivalence is isotopy. jean cerf proved that for simply connected smooth manifolds "m" of dimension at least 5, isotopy of "h"-cobordisms is the same as a weaker notion called pseudo-isotopy. hatcher and wagoner studied the components of the space of pseudo-isotopies and related it to a quotient of "k"(zπ).