4 problems

The conjecture. Under these hypotheses, the map

Let $X$ be a simply-connected finite space. Say that $X$ has a uniform $p$-torsion bound if there is an integer $N$ such that the $p$-primary torsion in every homotopy group of $X$…

Charming-map conjecture. The following statements are true:

The preceding constructions involve spectra $\mathbf L(i)\wedge \mathbf T(2^{n-i}-1)$, together with the spectra appearing in the complex of Theorem; the final cofibration has sourc…