7 problems

Let $\Gamma$ be a countable group acting minimally and topologically freely on a space $X$ by … , and let $\Gamma\ltimes X$ be the associated transformation groupoid. Write…

Maximal-subgroup classification conjecture. Exactly one of the following holds:

Higher-rank wreath-product non-embeddability conjecture. If $d\geq 2$, then

Higher-rank lamplighter non-embeddability conjecture. If $d\geq 2$, then

Lamplighter linear-look-ahead conjecture. The lamplighter group

AH conjecture. The index map $I$ should be surjective, and its kernel should be a quotient of

AH conjecture. There exists an exact sequence