10 problems

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 $E$ 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 ${\mathscr{F}}$ be a geometric oriented abelian sheaf over a derived stack $\mathsf{S}$. Write $\operatorname{Sp}_{\mathrm{fin}-\mathrm{gl}}$ for the symmetric monoidal…

For any Lie group $G$, let $G$-global stable homotopy theory denote the stable theory generalizing global and $G$-equivariant homotopy theory. Let … be the canonical functor, and l…

Let $\mathbf{bO}$ denote the global space that is the direct limit of the global classifying spaces $\mathbf B O(n)$, and regard $\mathbf{bO}$ also as an orbispace through the func…

Let $G$ be a finite group. Write $\mathbf B G\in\mathrm{OrbSpc}$ for its classifying orbispace and $\mathbf B G\in\mathrm{GloSpc}$ for the corresponding global classifying space. C…

Let $\mathrm{OrbSpc}$ be the category of orbispaces, let $\overline{\mathrm{OrbSpc}}$ be its enlargement obtained by gluing cells under arbitrary maps, and let $\mathrm{GloSpc}$ be…

Global-space full-faithfulness conjecture. For $X\in\mathrm{OrbSpc}^f$ and $F\in\mathrm{GloSpc}$, the set $\operatorname{Hom}(X,F)$ coincides with the morphisms from the image of…

Realization conjecture. The functor ${\mathbf K}_{\operatorname{gl}}$ should descend to an equivalence from the localization of ${\bf{ParSumCat}}$ at the class of…