arXiv subjects

Yu. B. Rudyak

Publications and source records attributed to Yu. B. Rudyak.

2 recordsLinked to original sources

arXiv2001

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

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.

math.GT↗

arXiv2000

Lusternik--Schnirelmann theory on general spaces

We extend Lusternik-Schnirelmann theory to pairs $(f, ϕ)$, where $ϕ$ is a homotopy equivalence of a space $X$, $f$ is a function on $X$ which decreases along $ϕ$ and $(f, ϕ)$ satisfies a discrete analog of the Palais-Smale condition. The theory is carried out in an equivariant setting.

math.DS↗