 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/24g/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

A covering evenly covers every base point. It is regular covering map when deck transformations act transitively on fibres. For a concrete nonregular example, restrict

z \mapsto z^{3} - 3 z

C ∖ p^{- 1} {- 2, 2} ⟶ C ∖ {- 2, 2} .

It is a surjective three-sheeted unbranched cover with monodromy

S_{3}

, so its deck group is not transitive.

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