Algebraic & Geometric Topology 4 (2004) 829–839

DOI: 10.2140/agt.2004.4.829

arXiv: math.AT/0410374

Abstract

Suppose the spaces X and X×A have the same Lusternik–Schnirelmann category: cat(X×A)=cat(X). Then there is a strict inequality cat(X×(A⋊B))<cat(X)+cat(A⋊B) for every space B, provided the connectivity of A is large enough (depending only on X). This is applied to give a partial verification of a conjecture of Iwase on the category of products of spaces with spheres.

Keywords

Lusternik–Schnirelmann category, Ganea conjecture, product formula, cone length

Mathematical Subject Classification

Primary: 55M30

References

Forward citations

Publication

Received: 6 March 2004
Accepted: 30 September 2004
Published: 7 October 2004

Authors