3 problems

Let $X$ be a simply connected finite CW complex whose cohomology with coefficients in ${\mathbb Z}/p{\mathbb Z}$ is non-trivial. Serre showed that $X$ has infinitely many non-zero…

Let $L$ be a finite $2$-complex equipped with a metric. A map is an $\varepsilon$-map if the pre-image of every point has diameter less than $\varepsilon$. Bestvina–Brady's conject…

Let $X$ be a simply connected finite CW complex, and let $p$ be a prime. Suppose that the cohomology of $X$ has non-trivial ${\mathbb{Z}}/p{\mathbb{Z}}$-cohomology. Serre's conject…