On the minimal number of critical points of functions on h-cobordisms

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62032Let (W,M,M'), dim W > 5, be a non-trivial h-cobordism (i.e., the Whitehead torsion of (W,V) is non-zero). We prove that every smooth function f: W --> [0,1], f(M)=0, f(M')=1 has at least 2 critical points. This estimate is sharp: W possesses a function as above with precisely two critical points.7 pages, LatexGeometric TopologyK-Theory and Homology57R80 (Primary) 19J10 57R10 (Secondary)On the minimal number of critical points of functions on h-cobordismstext