Geodesic
On Some Results in Morse Theory
Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 88-105

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Kalmbach, Gudrun. On Some Results in Morse Theory. Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 88-105. doi: 10.4153/CJM-1975-011-0
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