Arnold's seminar
Moscow University,
September 17, 2002

P. Pushkar'. Two theorems

1. Functions on manifolds having all critical points inside a ball.
2. On the minimal number of critical points of functions on h-cobordism.
(joint with Yu. Rudyak).

Dlya lyubikh dvukh svyaznykh zamknutikh mnogoobrazii s ravnoi eilerovoi
harakteristikoi suschestvuyut funkcii, sovpadayuschie na nekotorikh vlozhennykh
sharah, soderzhaschikh vse kriticheskie tochki.

Minimal'noe chislo kriticheskikh tochek funkcii na netrivial'nom svyaznom       
h-cobordisme bol'shoi razmernosti ravno dvum. (Funkciya ravna 0 na odnom i 1
na drugom krae).