Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 1, Number 1 (2001), 491-502.
The product formula for Lusternik–Schnirelmann category
If , denotes the mapping cone of an essential phantom map from the suspension of the Eilenberg–Mac Lane complex , to the –sphere , we derive the following properties: (1) The LS category of the product of with any –sphere is equal to ; (2) The LS category of the product of with itself is equal to , hence is strictly less than twice the LS category of . These properties came to light in the course of an unsuccessful attempt to find, for each positive integer , an example of a pair of –connected CW–complexes of finite type in the same Mislin (localization) genus with LS categories and If is such that its –localizations are inessential for all primes , then by the main result of [J. Roitberg, The Lusternik–Schnirelmann category of certain infinite CW–complexes, Topology 39 (2000), 95–101], the pair provides such an example in the case .
Algebr. Geom. Topol., Volume 1, Number 1 (2001), 491-502.
Received: 26 October 2000
Revised: 7 May 2001
Accepted: 17 August 2001
First available in Project Euclid: 21 December 2017
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Roitberg, Joseph. The product formula for Lusternik–Schnirelmann category. Algebr. Geom. Topol. 1 (2001), no. 1, 491--502. doi:10.2140/agt.2001.1.491. https://projecteuclid.org/euclid.agt/1513882605