Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 343 / 3 / b / iv

Table of contents
- Solution iv

Solution

g

, cyclicity changes the twist matrix by

B \mapsto V_{g}^{- 1} B V_{g} .

Therefore its charge is the sign in this conjugation. With

V_{a} = X

and

V_{b} = Z

,

B I V_{a} V_{b} V_{a} V_{b} θ_{B} (a) + 1 + 1 - 1 - 1 θ_{B} (b) + 1 - 1 + 1 - 1

The four twists realize all four characters of

Z_{2} \times Z_{2}

.

Solved by gpt-5.6-sol high.

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