Abstract
The /z-cobordism theorem in [8], the generalized Poincaré conjecture in higher dimensions in [20] and several other results in differential topology are proved by using the following theorems of Morse theory:(1) the elimination of critical points;(2) the existence of nondegenerate functions for which the descending and ascending bowls have normal intersection;(3) the alteration of function values at critical points. (For the details see below.)We shall give short and elementary pr∞fs of these theorems together with some stronger statements than the ones given in [8-13] or [19].The theorems are proved for noncompact manifolds rather than for compact manifolds since, by a trivial modification of the manifold (deleting the boundary or one point) the case of compact manifolds is included.
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