On the minimal number of critical points of functions on h-cobordisms
Geometric Topology
2007-05-23 v1 K-Theory and Homology
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.
Cite
@article{arxiv.math/0108115,
title = {On the minimal number of critical points of functions on h-cobordisms},
author = {P. E. Pushkar and Yu. B. Rudyak},
journal= {arXiv preprint arXiv:math/0108115},
year = {2007}
}
Comments
7 pages, Latex