5 problems

Coarse Baum–Connes conjecture. The rational Roe index map is an equivariant split monomorphism. This version is described as a further coarsening of the condition $FW$ and as imply…

Let $A$ be a filtered $C^{\ast}$-algebra, let $X$ be a proper metric space, and let $N_X$ be a locally finite net in $X$. Let $\bigsqcup_{\mathbb{N}}X_i$ denote the separated coars…

Let $X$ be a metric space with bounded geometry, let $P_d(X)$ be its Rips complex at scale $d$, and let $\Gamma(X,\mathcal A)$ be a coarse $X$-algebra. The twisted assembly map is…

The warped-cone assembly conjecture. The coarse assembly map is not surjective for the warped cone $X=\mathcal{O}_G M$. This would provide a geometric obstruction to the coarse Bau…

A warped cone is the metric space associated to an action of a finitely generated group $G$ on a compact metric probability space $M$ as above; when the action has a spectral gap,…