Mimicking the Lusternik-Schnirelmann category invariant for a smooth manifold we can ask about the minimal number of critical loops of smooth scalar maps which are round functions, that is functions whose critical points are aligned in a disjoint union of closed curves (a link).
This number is called the round complexity of and it is symbolized as
This concept is related to the invariant called t-cat.
Theorem 2: For each closed manifold,
D. Siersma, G. Khimshiasvili, On minimal round functions, Preprint 1118, Department of Mathematics, Utrecht University, 1999, pp. 18.
|Date of creation||2013-03-22 15:54:52|
|Last modified on||2013-03-22 15:54:52|
|Last modified by||juanman (12619)|