4 problems

Let $A$ be a filtered $C^{\ast}$-algebra, let $X$ and $Y$ be proper metric spaces, and let $N_X$ be a locally finite net in $X$. For each $k\geq 0$, let $P_k(N_X)$ be the $k$-Rips…

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…