Implications of the Ganea Condition
Algebraic Topology
2014-10-01 v2
Abstract
Suppose the spaces X and X cross A have the same Lusternik-Schnirelmann category: cat(X cross A)= cat(X). Then there is a strict inequality cat(X cross (A halfsmash B)) < cat (X) + cat(A halfsmash 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.
Cite
@article{arxiv.math/0410374,
title = {Implications of the Ganea Condition},
author = {Norio Iwase and Donald Stanley and Jeffrey Strom},
journal= {arXiv preprint arXiv:math/0410374},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-36.abs.html