On a lower bound for the \(L\)-\(S\)-category of a rationally elliptic space. (English) Zbl 1134.55300

Yamaguchi, Toshihiro

Bull. Belg. Math. Soc. - Simon Stevin 12, No. 4, 565-568 (2005).

The author proves a formula giving a lower bound for the \(L\)-\(S\)-category of a rationally elliptic space in terms of the dimension of its rational cohomology: Theorem 1.1 if \(X\) is elliptic with rank \(\pi_{\text{even}}(X)\leq 1\), then \(\dim H^*(X;\mathbb Q)\leq 2^{\text{cat}(x)}\).

MSC:

55M30	Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects)
55P62	Rational homotopy theory

Keywords:

Sullivan minimal model