Lusternik--Schnirelmann theory on general spaces

Abstract

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

23 pages, 1 figure