A minimal triangulation of complex projective plane admitting a chess colouring of four-dimensional simplices
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2009
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| _version_ | 1866916487151747072 |
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| author | Gaifullin, Alexander A. |
| author_facet | Gaifullin, Alexander A. |
| contents | In this paper we construct and study a new 15-vertex triangulation $X$ of the complex projective plane $\CP^2$. The automorphism group of $X$ is isomorphic to $S_4\times S_3$. We prove that the triangulation $X$ is the minimal by the number of vertices triangulation of $\CP^2$ admitting a chess colouring of four-dimensional simplices. We provide explicit parametrizations for 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 provide a 33-vertex subdivision $\bX$ of the triangulation $X$ such that the classical moment mapping $μ:\CP^2\toΔ^2$ is a simplicial mapping of the triangulation $\bX$ onto the barycentric subdivision of the triangle $Δ^2$. We study the relationship of the triangulation $X$ with complex crystallographic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0904_4222 |
| institution | arXiv |
| publishDate | 2009 |
| record_format | arxiv |
| spellingShingle | A minimal triangulation of complex projective plane admitting a chess colouring of four-dimensional simplices Gaifullin, Alexander A. Geometric Topology Metric Geometry 52B70, 20H15 In this paper we construct and study a new 15-vertex triangulation $X$ of the complex projective plane $\CP^2$. The automorphism group of $X$ is isomorphic to $S_4\times S_3$. We prove that the triangulation $X$ is the minimal by the number of vertices triangulation of $\CP^2$ admitting a chess colouring of four-dimensional simplices. We provide explicit parametrizations for 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 provide a 33-vertex subdivision $\bX$ of the triangulation $X$ such that the classical moment mapping $μ:\CP^2\toΔ^2$ is a simplicial mapping of the triangulation $\bX$ onto the barycentric subdivision of the triangle $Δ^2$. We study the relationship of the triangulation $X$ with complex crystallographic groups. |
| title | A minimal triangulation of complex projective plane admitting a chess colouring of four-dimensional simplices |
| topic | Geometric Topology Metric Geometry 52B70, 20H15 |
| url | https://arxiv.org/abs/0904.4222 |