A topic within Topology, itself one of 11 topics in that field and part of Mathematics.
2 works
John Milnor
Shows that the topology of a manifold is controlled by the critical points of any sufficiently generic smooth function on it, turning the classification of manifolds into a study of critical-point behaviour.
Raoul Bott
Surveys how the idea that a function's critical points control a manifold's topology grew from Morse's original inequalities into later applications in gauge theory and loop spaces.
link checked 17 Sept 2026