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

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

2001-08-16

arxiv.org/abs/math/0108115v1

Mathematics

Geometric Topology

7 pages, Latex

Scientific paper

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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