# zbMATH — the first resource for mathematics

Homotopy exponents for spaces of category two. (English) Zbl 0671.55009
Algebraic topology, Proc. Int. Conf., Arcata/Calif. 1986, Lect. Notes Math. 1370, 24-52 (1989).
[For the entire collection see Zbl 0661.00012.]
A space X is said to have an exponent at the prime p if and only if there exists an integer $$r>0$$ such that for all n, multiplication by $$p^ r$$ annihilates the p-torsion of $$\pi_ n(X)$$. The author proves the following weakened from of Moore’s conjecture: Let X be a simply- connected finite complex of Ljusternik-Schnirelmann category two. There is a finite set P of primes such that: (a) If dim $$\pi_*(X)\otimes {\mathbb{Q}}<\infty$$, then X has an exponent at every $$p\not\in P$$, (b) If dim $$\pi_*(X)\otimes {\mathbb{Q}}=\infty$$, then X fails to have an exponent at any $$p\not\in P$$.
Reviewer: Y.Felix

##### MSC:
 55Q05 Homotopy groups, general; sets of homotopy classes 55P62 Rational homotopy theory 55M30 Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects)