There does not exist an isomorphism-invariant Borel map which selects a just-infinite quotient of each infinite finitely generated group.

Let $M$ be a smooth manifold. When $\Gamma$ is group acting on the manifold by diffeomorphisms one can define $\Gamma$-co-invariant cohomology of to differential complex $\Omega_c(M)_\Gamma=\mathrm{span}\{\omega-\gamma^*\omega,\;\omega\in\Omega_c(M),\;\gamma\in\Gamma\}.$ For Lie algebra $\mathcal{G}$ $M$, defines $\mathcal{G}$-divergence forms $\mathcal{C}_{\mathcal{G}}(M)=\mathrm{span}\{L_X\om...

In recent years there has been a growing interest in treating many-body systems as Bell scenarios, where lattice sites play the role of distant parties and only near-neighbor statistics are accessible. We investigate contextuality arising from three scenarios infinite, translation-invariant 1D models: nearest-neighbor with two dichotomic observables per site; nearest- next-to-nearest neighbor s...