7 problems

Let $G$ be an algebraic group over $\mathbb R$, let … and let $p$ be a prime number. Regard $G(\mathbb C)$ as a $\Gamma$-space and let $G(\mathbb C)^{\operatorname{top}}$ denote it…

Let $G=C_2$. A $\operatorname{Rep}(C_2)$-complex is a $C_2$-space built by attaching cells of the form $D(\mathbf R^{p,q})$, where $p\geq q\geq0$; it is of finite type if, for each…

Family-stabiliser tree conjecture. The inequality $\operatorname{cd}_{\mathcal{F}}G\leqslant 1$ holds if and only if $G$ acts on a tree whose stabilisers generate $\mathcal{F}$.

Let $\mathfrak{F}$ be the class of finite groups. A group $G$ belongs to ${\scriptstyle \mathbf H}_{1}\mathfrak{F}$ if it admits a finite-dimensional contractible $G$-…

Finiteness equivalence conjecture.

Let $\mathfrak{F}$ be the class of finite or virtually cyclic groups. Kropholler's class ${{\scriptstyle\bf H}}\mathfrak{F}$ and the generalized class…

Let $G$ be a group and let $\frakF$ be a semi-full family of subgroups of $G$. Write $\cd_{\frakF}G$ for the Bredon cohomological dimension and $\gd_{\frakF}G$ for the Bredon geome…