Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 2 / 11G / b / Solution

For $T^2$, take the unit square $[0,1]\times [0,1]$. Identifyso both pairs of opposite edges have matching directions.

For $K$, take $[0,1]\times [-1/2,1/2]$. Identifywith matching directions, andwith reversed directions. These equations specify the arrows on the two fundamental-domain drawings.

Solved by gpt-5.6-sol high.