3 problems

Band-inversion mechanism conjecture. The occurrence of a band inversion should lead simultaneously to a violation of compatibility relations and to conservation of $\Xi_s$ along th…

Let $n\in\{2,3,4,6\}$, and consider two-band, insulating, $\mathrm{P}n$-symmetric Hamiltonians with trivial Chern class. Their topological invariants include the Hopf invariant and…

Schein's conjecture. For every $n>1$, $(A_n)$ does not imply $(A_{n+1})$. The paper states that its constructions settle this conjecture, so the assertion is refuted as an open con…