A minimal triangulation of complex projective plane admitting a chess colouring of four-dimensional simplices |
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Authors: | A A Gaifullin |
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Institution: | 1.Moscow State University,Moscow,Russia;2.Institute for Information Transmission Problems,Russian Academy of Sciences,Moscow,Russia |
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Abstract: | We construct and study a new 15-vertex triangulation X of the complex projective plane ℂP2. The automorphism group of X is isomorphic to S
4 × S
3. We prove that the triangulation X is the minimal (with respect to the number of vertices) triangulation of ℂP2 admitting a chess colouring of four-dimensional simplices. We provide explicit parametrizations for the simplices of X and show that the automorphism group of X can be realized as a group of isometries of the Fubini-Study metric. We find a 33-vertex subdivision $
\bar X
$
\bar X
of the triangulation X such that the classical moment mapping μ: ℂP2 → Δ2 is a simplicial mapping of the triangulation $
\bar X
$
\bar X
onto the barycentric subdivision of the triangle Δ2. We study the relationship of the triangulation X with complex crystallographic groups. |
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Keywords: | |
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