3 problems

Let $n$ be a positive integer. The group $\mathcal{Z}_n((\mathbb{Z}_2)^n)$ is the group of $n$-dimensional equivariant unoriented bordism classes for the action of…

Vanishing Stiefel–Whitney classes conjecture. The first $2^{t+1}-1$ Stiefel–Whitney classes of $M$ vanish if and only if, for every $S\subseteq\{1,2,\ldots,k\}$ with $|S|\leq t+1$,…

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…