5 problems

Stable non-nullity conjecture. For any quasitoric manifold $M$, $\Sigma^\infty\pi$ is not null homotopic.

Let $P^n$ be a simple convex $n$-dimensional polytope that admits a proper coloring with $n$ colors. Let $\alpha(n)$ denote the number of $1$'s in the binary expansion of $n$, and…

Let $\mathcal{Z}_{2n}^{U}(T^n)$ be the group of $T^n$-equivariant unitary bordism classes of $2n$-dimensional unitary toric manifolds, let $\mathcal{Q}_*$ be the graded noncommutat…

Buchstaber–Panov–Ray 12-dimensional assertion. Every 12-dimensional specially omnioriented quasitoric manifold is bordant to zero in $\Omega_{12}^U$.

Buchstaber–Panov–Ray conjecture. $M^{2n}$ represents the zero element in $\Omega_{2n}^U$.