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Given a triangulation, how do we tell which space it is representing?

My first idea would be to calculate the Euler Characteristic, but that would still leave some ambiguity, e.g. both the Projective Plane and the Disk have Euler Characteristic 1.

Thanks!

Also, does any Algebraic Topology textbook covers in depth on Triangulation and Euler Characteristic? Most of the books I have read thus far (Munkres, Hatcher, etc.) do mention it but only briefly.

yoyostein
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  • You should maybe look into some literature concerning random triangulations. They usually discuss how the triangulation would be chosen to get e.g. a closed manifold (which would rule out the disk). They also of course discuss properties of labeled triangulations. – Daniel Valenzuela Aug 31 '15 at 09:49

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