3 problems

The homological $n$-$(n+1)$-$(n+2)$ conjecture. If $N_{1}$ is of type $\operatorname{FP}_n$, $G_1$ and $G_2$ are of type $\operatorname{FP}_{n+1}$, and $Q$ is of type…

The $n$-$(n+1)$-$(n+2)$ conjecture. If $N_{1}$ is of type $\operatorname F_n$, $G_1$ and $G_2$ are of type $\operatorname F_{n+1}$, and $Q$ is of type $\operatorname F_{n+2}$, then…

The $n$-$(n+1)$-$(n+2)$ conjecture. If $N_1$ is of type $\operatorname{F}_n$, both $\Gamma_1$ and $\Gamma_2$ are of type $\operatorname{F}_{n+1}$, and $Q$ is of type…