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

P. E. Pushkar; Yu. B. Rudyak

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

P. E. Pushkar·Yu. B. Rudyak

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Abstract

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.

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BibTeX RIS

P. E. Pushkar, Yu. B. Rudyak. 2001-08-16. On the minimal number of critical points of functions on h-cobordisms. https://arxiv.org/abs/math/0108115

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