#### Volume 20, issue 1 (2020)

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Lusternik–Schnirelmann category of products with half-smashes

### Don Stanley and Jeff Strom

Algebraic & Geometric Topology 20 (2020) 439–450
##### Abstract

We show that for a fixed space $X$ and any sufficiently highly connected space $A$ ($conn\left(A\right)>dim\left(X\right)$ is more than enough), the Lusternik–Schnirelmann category of products with $X$ is remarkably stable with respect to changes in the second variable:

Taking $X={S}^{n}$ leads to a closure property for the collections of spaces which do or do not satisfy the Ganea condition $cat\left({S}^{n}×A\right)=1+cat\left(A\right)$.

##### Keywords
Lusternik–Schnirelmann category, half-smash, Ganea conjecture, Ganea condition, cartesian product, homotopy theory
Primary: 55M30