8 problems

Let $W$ be an infinite Coxeter group, let $Y_W$ be the associated hyperplane complement in $\mathbb{C}\otimes V$ restricted to the Tits cone, and let $A$ be the associated Artin gr…

Non-positive surface curvature implies asphericity. If $\sigma_+(X)\leq 0$ then $X$ is aspherical.

Let $X$ be an aspherical 2-complex, and let $Y$ be a subcomplex of $X$. Whitehead's conjecture. The subcomplex $Y$ is aspherical. This is a famous conjecture about asphericity inhe…

Let $l>0$ and $k>0$ with $l\neq k$, and let $\mathcal{Q}$ be the relative presentation considered in the paper. Define condition (AEJ-E) by the following alternatives: (i) $g=h^2$,…

Let $\mathcal{Q}$ be the relative presentation considered in the paper, with parameters $l>0$, $k\neq 0$ and non-trivial elements $g,h\in G$. Define … Say that Case $(P)$ holds whe…

Let $\Phi$ be a reduced root system with Weyl arrangement $\mathscr A(\Phi)$. An arrangement of ideal type $\mathscr A_{\mathcal I}$ is a subarrangement of $\mathscr A(\Phi)$ deter…

Ivanov's asphericity conjecture. Then $\mathcal{Q}$ is aspherical.

Let an arrangement be a collection of weighted lines in $\mathbb{CP}^2$ satisfying the conditions of Theorem existence. Its complement is the space obtained by removing the arrange…