Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 133 / 1 / a / Solution

For a finite group presentation $⟨S\mid R⟩$ and a word $w\in F(S)$ representing the identity, the area of a null-homotopic word isThe Dehn function of the presentation isEquivalently, area is the least number of two-cells in a van Kampen diagram for $w$, and the Dehn function is the worst such area among null words of length at most $n$.

Solved by gpt-5.6-sol high.