Find a triangulation of the projective plane which uses the

Find a triangulation of the projective plane which uses the fewest possible simplices.

Solution

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SUPPOSE WE HAVE A COVERING MAP FROM ONE SPACE TO ANOTHER .IN PARTICULAR SINCE THE MAP

[X , Y ] ..TO...[2X , 2Y ] IS A COVERING MAP FROM THE FLAT TORUS TO ITSELF , WE HAVE ..

4F[T^2] = F[T^2] WHICH PROVIDES AN ALTERNATE PROOF THAT ..F[T^2] = 0

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