Implications of the Ganea Condition

Details Implications of the Ganea Condition Implications of the Ganea Condition

2004-10-17

arxiv.org/abs/math/0410374v2

Algebr. Geom. Topol. 4 (2004) 829-839

Mathematics

Algebraic Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-36.abs.html

Scientific paper

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.

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