8 problems

HK conjecture. For $* = 0,1$, there is an isomorphism

Let $\mathcal{G}$ be a second countable, étale groupoid, and let $\widehat{\mathcal{G}}$ be the blow-up groupoid with base-related notation $\widehat{X}$. Suppose that $c$-…

Let $\mathcal{G}$ be a second countable, locally compact, Hausdorff, étale groupoid, and let $\widehat{\mathcal{G}}$ be its blow-up at torsion elements of isotropy groups. Write…

Rational HK-conjecture. One should have

HK-realization conjecture. There should exist a possibly different groupoid $\widetilde{\mathcal{G}}$ such that

Let $E$ and $F$ be finite graphs, and let $R$ be a field. Write $\mathcal{G}_E$ and $\mathcal{G}_F$ for their graph groupoids, and let $H_0^{\operatorname{gr}}$ denote graded group…

AH conjecture. There exists an exact sequence

HK conjecture. The even and odd homology groups of $\mathcal{G}$ satisfy