63 problems

Intermediate-differential conjecture. For $j\gg k>0$,

Let $Q_8$ be the quaternion group, let $C_2$ be its indicated subgroup, and let $N_{C_2}^{Q_8} MU\mathbb{R}$ denote the quaternionic norm of real bordism. For a subgroup $L$ of…

Disklike characterization conjecture. The maximal compatible transfer system is

Let $G$ be the group acting in the hyperreal setting, let $C_2$ be its indicated subgroup, and let $E_{2+\sigma}$ and $BBU_{\mathbb R}$ denote the spaces appearing in the source. W…

Abelianness conjecture for saturated groups. If $G$ is a saturated finite group, then $G$ is abelian.

Let $C_2$ be the cyclic group of order two, let $\operatorname{MSpin}^c_{\operatorname{\mathbb{R}}}$ denote Real spin bordism, let $\mathcal{P}$ be the indexing set for the Anderso…

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 $G$ be a finite group. A pair of $G$-transfer systems is called compatible when it satisfies the compatibility conditions for a pairing of $N_{\infty}$-operads, and it is reali…

Malkiewich–Ponto's conjecture. The fiberwise Fuller trace

Let $G$ be a finite group. The equivariant $SK^G$-groups, as $H$ varies over the subgroups of $G$, form a Mackey functor, and let $K_G(\underline{\mathbb{Z}})$ denote the genuine…

Let $\mathbf{R}$ denote the Real global group law constructed from the Real globally oriented spectrum $\mathbf{MR}$. For each torus $\mathbb{T}^n$, let…

Let $G$ be a compact quasi-abelian Lie group equipped with an augmentation … Write $\rho$ for the relevant regular representation and $M\mathbb{R}_\eta$ for the associated Real equ…

Let $\Gmr$ be a finite group and let $\upalpha$ be an indexing representation. Let $\Ecal_{\Gmr, {\bf 0}}^{\Sigma, {\sf conn}}$ be the category of connected-at-infinity equivariant…

Let $\Gmr$ be a finite group, and let ${\bf B}_{\Gmr}{\bf Top}^{(1)}$ denote the first layer of the equivariant Weiss functor ${\bf B}_{\Gmr}{\bf Top}$. Suppose there exists an inc…

Let $S/(h,v^4_{(1,0)})$ denote the indicated $C_2$-equivariant complex, let $a$ be the Euler-class element, and let $\widetilde{\bar{\kappa}}$ denote the specified equivariant lift…

Suppose that $X\in\mathrm{Sp}^{C_2}_{(2),\omega}$ is a type $(n,n-1)$ complex. Suppose further that the modified inductive procedure produces a $v_n$-self map as a Mahowald invaria…

Odd-prime transchromatic shearing conjecture. There is a shearing isomorphism

Surjectivity conjecture. For all $m\geq 1$ and $r\geq 2$, this map induces a surjection on the $\mathcal{E}_r$-page and on the $d_r$-differentials.

Height classification conjecture. The $C_{2^n}$-slice spectral sequence of $BP^{(C_{2^n})}\langle m\rangle$ contains all differentials in the slice spectral sequence of…

Hill–Hopkins–Ravenel transchromatic phenomenon. The slice spectral sequences of higher height theories contain isomorphism regions to the slice spectral sequences of lower height t…

Equivariant monoid realization conjecture. Any $G$-connected based $G$-space $X$ is weakly equivalent to

Let $G$ be a compact Lie group, let $MU_G$ denote $G$-equivariant complex cobordism, and let $KU_G$ denote equivariant complex K-theory. The relative smash product…

Let $A$ be a compact abelian Lie group, let $B$ be a subgroup of $A$, let $E$ be a Landweber exact spectrum, and let $\Phi^B$ denote geometric fixed points. For an $A$-space or $A$…

Let $E$ be a Landweber exact spectrum, and let $\mathbf{MU}$ denote the global equivariant analogue of complex cobordism. A global version of May's functor would assign to $E$ the…

Let $E$) be a Landweber exact spectrum, let $A$ be a compact abelian Lie group, and let $MU_A$ denote equivariant complex cobordism for $A$. The relative smash product…