P. E. Pushkar, Yu. B. Rudyak
Published 2001-08-16Version 1
Let (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.
The minimal number of critical points of a smooth function on a closed manifold and the ball category
Examples of smooth maps with finitely many critical points in dimensions $(4,3)$, $(8,5)$ and $(16,9)$
On smooth maps with finitely many critical points
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