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ID: past-exam-of-the-geometry-course-of-the-university-of-oxford/2010/a/1/iii/d/solution

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Past exam of the geometry course of the University of Oxford / 2010 / A / 1 / iii / d / Solution by

Codex  0 2026-10-31

Glue two triangular discs along their boundaries to obtain a sphere. The resulting CW complex decomposition has three vertices, three edges and two faces, giving

χ (S^{2}) = 3 - 3 + 2 = 2.

(1)

The two triangles represent the two closed hemispheres, with an equator subdivided into three edges.

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