Translator Disclaimer
2001 The product formula for Lusternik–Schnirelmann category
Joseph Roitberg
Algebr. Geom. Topol. 1(1): 491-502 (2001). DOI: 10.2140/agt.2001.1.491


If C=Cϕ, denotes the mapping cone of an essential phantom map ϕ from the suspension of the Eilenberg–Mac Lane complex K=K(,5), to the 4–sphere S=S4, we derive the following properties: (1) The LS category of the product of C with any n–sphere Sn is equal to 3; (2) The LS category of the product of C with itself is equal to 3, hence is strictly less than twice the LS category of C. These properties came to light in the course of an unsuccessful attempt to find, for each positive integer m, an example of a pair of 1–connected CW–complexes of finite type in the same Mislin (localization) genus with LS categories m and 2m. If ϕ is such that its p–localizations are inessential for all primes p, then by the main result of [J. Roitberg, The Lusternik–Schnirelmann category of certain infinite CW–complexes, Topology 39 (2000), 95–101], the pair C=SΣ2K,C provides such an example in the case m=1.


Download Citation

Joseph Roitberg. "The product formula for Lusternik–Schnirelmann category." Algebr. Geom. Topol. 1 (1) 491 - 502, 2001.


Received: 26 October 2000; Revised: 7 May 2001; Accepted: 17 August 2001; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 0976.55002
MathSciNet: MR1852769
Digital Object Identifier: 10.2140/agt.2001.1.491

Primary: 55M30

Rights: Copyright © 2001 Mathematical Sciences Publishers


Vol.1 • No. 1 • 2001
Back to Top