13 problems

Let ${\mathcal H}^?_*$ be an equivariant homology theory with values in $R$-modules, let $G$ be a group, and let ${\mathcal C}$ be a family of subgroups of $G$. Let…

Let $G$ be a group, let $E_{\mathcal{VCY}}(G)$ be the classifying $G$-space for the family of virtually cyclic subgroups, and let $\mathcal{A}$ be an additive $G$-category with inv…

Let $\Gamma$ be a countable group acting properly and isometrically on the Euclidean space $\mathbb{E}_{\Gamma}$, and let $\mu_{\mathrm{IP}}$ denote the assembly map for the equiva…

Let $Y$ be a rational homology sphere, let $E$ be the bundle used to define the equivariant instanton complex, let $R$ be the coefficient ring, and let $\sigma$ be a choice of sign…

Stable-envelope existence and uniqueness conjecture. There exist unique classes $(S_p)_{p\in\mathfrak M_1^T}$ in $H_{\dim\mathfrak Z}^T(\mathfrak M_1)$ such that, for every…

Let $\mathcal{P}$ be the Procesi bundle on $\operatorname{Hilb}^n(\mathbb{C}^2)$, let $\mathcal{P}^*$ denote its dual, and let $\mathcal{O}(d)$ be the indicated determinant-line-bu…

Let ${\mathbf S}\colon\operatorname{SPACES}\to\operatorname{SPECTRA}$ respect weak equivalences and disjoint unions. Let $G$ be a group and ${\mathcal F}$ a family of subgroups of…

Let $\Gamma$ be a group, let $(G,\psi)$ be a group over $\Gamma$ with homomorphism $\psi\colon G\to\Gamma$, let ${\mathcal H}^?_*$ be an equivariant homology theory over $\Gamma$,…

Let ${\mathbf S}\colon\operatorname{SPACES}\to\operatorname{SPECTRA}$ be a covariant functor respecting weak equivalences and disjoint unions. Let ${\mathcal C}$ be a class of grou…

Let ${\mathbf S}\colon\operatorname{SPACES}\to\operatorname{SPECTRA}$ be a covariant functor respecting weak equivalences and disjoint unions. Let $G$ be a group, ${\mathcal F}$ a…

Let ${\mathbf S} \colon \operatorname{SPACES}\to \operatorname{SPECTRA}$ be a covariant functor respecting weak equivalences and disjoint unions. For a group $G$, let…

Let $\cF$ be a family of groups, let $G$ be a countable discrete group, and let $W$ be a free $G$-CW-complex. Let $E_\cF G$ denote the classifying space of $G$ for the family $\cF$…

Meta-isomorphism conjecture. The assembly map $A_{\mathcal{F}}$ is an isomorphism for every $n\in\mathbb{Z}$.