 Solution

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

A polygonal model of the real projective plane is a bigon with boundary word

aa

, with the equally labelled arrows identified. Its two vertices become one, its sides form one edge, and it has one face. Thus

χ (P) = 1 - 1 + 1 = 1.

Equivalently, glue antipodal boundary points of a disc.

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