9 problems

Let $\mathcal{P}_{6,48}$ be the centrally symmetric simplicial $6$-polytope whose antipodal quotient of the boundary gives a triangulation of $\mathbb{R}P^5$. A triangulation is ve…

For each positive integer $n$, define … Let $X$ be a finite CW-complex whose mod-$2$ cohomology is that of $\prod_{i=1}^k\mathbb{R}P^{n_i}$. Suppose that $G=(\mathbb{Z}/2)^r$ acts…

Let $n_1,\ldots,n_k$ be natural numbers, and define … Suppose $(\mathbb{Z}_2)^r$ acts freely and mod $2$ cohomologically trivially on…

Let $\operatorname{Imm}(X)$ denote the immersion dimension of a space $X$. For every integer $a\geq2$, consider the real projective space $\operatorname{\mathbb{R}P}^{2^a+2^{a+1}}$…

Monotonicity conjecture. For every integer $j$ with $2\leq j\leq r(2^a+2^{a+1})$,

Let $m$ be a positive integer such that $m+1$ is not a power of $2$. Set $e=e(m)$, let $r(m)$ be the integer defined from the sequence $d_0,\ldots,d_t$ and coefficients…

For $m\geq1$ and $s\geq2$, let $G_s(m)=sm-\operatorname{zcl}_s(\operatorname{\mathbb{R}P}^m)$, and let $e(m)$ be determined by … The sequence $G_s(m)$ stabilizes to $G(m)$. The sta…

Assume $m\equiv2^e-1\pmod{2^{e+1}}$ with $e\geq0$, so $e$ is the length of the block of consecutive ones ending the binary expansion of $m$. Let…

Let $\mathbb{R}P^4_{16}$ denote the constructed $16$-vertex triangulation of the real projective $4$-space $\mathbb{R}P^4$. Uniqueness conjecture. $\mathbb{R}P^4_{16}$ is the uniqu…