A torsion-free hyperbolic group that is neither residually finite nor linear over any field
What the paper claims, in its own words
Constructs a torsion-free word-hyperbolic group that is not residually finite, answering the residual-finiteness question negatively. One fixed nonidentity element is killed by every finite-dimensional linear representation over every commutative field, so the group is not linear over any such field.
The plain-language explainer for this entry is still coming.
The original paper
- A torsion-free hyperbolic group that is not residually finite (PDF, opens in a new tab) September 23, 2026 Formal proof listed