10 problems

Intrinsic-bracket conjecture. The homomorphism $I$ induces an isomorphism of operads

Let $\Gmr$ be a finite group and let $p$ be a prime. For each $i$, let $\Ecal^{(p^i)}_{\Gmr,p}$ be the collection of integral $\uprho_{\Gmr}$-stable $\Hmr\underline{\FF}_p$-Euleria…

Let $X^n$ be a space and let $p$ be a prime. Say that $H^*(X;\mathbb{Z}_p)$ is $k$-periodic up to degree $c$ when multiplication by a periodicity element induces successive isomorp…

Let $X$ be a topological space and let $p$ be an odd prime. A nonzero element $x\in H^k(X;\mathbb{Z}_p)$ induces periodicity if multiplication by $x$ gives isomorphisms … for all…

Let $X$ be a connected topological space. A nonzero element $x\in H^k(X;\mathbb{Z}_2)$ induces periodicity if multiplication by $x$ gives isomorphisms … for all $i\geq 0$; in this…

Let ${\mathtt P}=[n]$, and let $\overline{p}$ and $\overline{q}$ be Goresky–MacPherson perversities. Let ${\mathtt K}(R,n,{\mathtt P},\overline{p})$ denote the perverse Eilenberg–M…

Let $k_2o\langle r\rangle$ denote the indicated connective twisted $KO$-theory spectrum, let $\underline{\mathcal A(1)}$ be the twisted Steenrod subalgebra, let $\varphi$ be the em…

Let $X$ be a space and let $n>2$. Assume that $LS_2(X)\leq n-2$, where $LS_2$ is the local LS-category invariant defined using an $n$-set cover whose pairwise unions map null homot…

Let $p$ be a prime, let $M$ be a topological space, and let $x\in H^k(M;\mathbb{Z}_p)$ be nonzero. Say that $x$ induces periodicity up to degree $r$ when multiplication by $x$ give…

Let $R=\mathbb{Z}/p^2$, and let $\mathcal{M}^N$ be the category of finitely generated free graded $R$-modules concentrated in degree less than $N$. For a bigraded differential alge…