作用于CAT（0）空间的群的E_{vc}和E_{fbc}的构造

作用在CAT（0）-空间上群的Bredon上同调维数

Bredon cohomological dimensions for groups acting on CAT(0)-spaces

设G是拓扑维数有界的可分完备CAT（0）-空间上具有离散轨道的等距作用群。在一定条件下，给出了有限子群族和虚循环子群族G的Bredon上同调维数的上界.作为应用，我们证明了亏格g大于1的任意闭连通可定向曲面的映射类群允许一个具有虚循环稳定子的（9 g-8）维分类空间.此外，我们的结果适用于基本群的图形的群体和群体的欧几里德建筑物。特别地，我们证明了所有正特征的非线性生成的线性群对于真作用有一个有限维的分类空间，对于虚循环子群族有一个有限维的分类空间.我们还表明，每个广义Baumslag-Solitar群有一个3维模型的分类空间与虚拟循环稳定。

H空间的拓扑复杂性

Topological Complexity of H-Spaces

设X是一个（不一定是同伦结合的）H-空间。我们证明了TC_{n+1}（X）= cat（X^n），其中n >= 1，其中TC_{n+1}（-）表示Rudyak引入的所谓高拓扑复杂性，cat（-）表示Lusternik-Schnirelmann范畴.我们还将这个等式推广到一个不等式，它给出了在空间Y作用于X上时TC_{n+1}（X）的上界。

An alternate description of equivariant connections

In this note, we consider a Lie group G acting on a manifold M. We prove that the category of bundles with connection on the differential quotient stack is equivalent to the category of G-equivariant bundles on M with G-invariant connection.

Bredon cohomological dimension for virtually abelian stabilisers for CAT(0) groups

Given a discrete group $G$, for any integer $r\geqslant0$ we consider the family of all virtually abelian subgroups of $G$ of rank at most $r$. We give an upper bound for the Bredon cohomological dimension of $G$ for this family for a certain class of groups acting on $\mathrm{CAT}(0)$ spaces. This covers the case of Coxeter groups, Right-angled Artin groups, fundamental groups of special cube complexes and graph products of finite groups. Our construction partially answers a question of J.-F. Lafont.

Motivic spectral Mackey functors

We show that if G is a finite constant group acting on a scheme X such that the order of G is invertible in the residue fields of X, then the G-equivariant motivic stable homotopy category of X is equivalent to the stabilization of the category of motivic G-spaces with finite étale transfers over X at the trivial representation sphere. Along the way we obtain several results of independent interest, among them: we construct and study norms in the motivic homotopy theory of stacks, and we extend the homotopy t-structure to DM-stacks and establish some favorable properties.