Some $\ZZ_3^n$-equivariant triangulations of $\CP^n$
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arXiv
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| Formato: | Preprint |
| Publicado: |
2014
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| _version_ | 1866911143161757696 |
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| author | Sarkar, Soumen |
| author_facet | Sarkar, Soumen |
| contents | In 1983, Banchoff and Kuhnel constructed a minimal triangulation of $\CP^2$ with 9 vertices. $\CP^3$ was first triangulated by Bagchi and Datta in 2012 with 18 vertices. Known lower bound on number of vertices of a triangulation of $\CP^n$ is $1 + \frac{(n + 1)^2}{2}$ for $n \geq 3$. We give explicit construction of some triangulations of complex projective space $\CP^n$ with $\frac{4^{n+1}-1}{3}$ vertices for all $n$. No explicit triangulation of $\CP^n$ is known for $n \geq 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1405_2568 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Some $\ZZ_3^n$-equivariant triangulations of $\CP^n$ Sarkar, Soumen Geometric Topology 05E18, 57Q15 In 1983, Banchoff and Kuhnel constructed a minimal triangulation of $\CP^2$ with 9 vertices. $\CP^3$ was first triangulated by Bagchi and Datta in 2012 with 18 vertices. Known lower bound on number of vertices of a triangulation of $\CP^n$ is $1 + \frac{(n + 1)^2}{2}$ for $n \geq 3$. We give explicit construction of some triangulations of complex projective space $\CP^n$ with $\frac{4^{n+1}-1}{3}$ vertices for all $n$. No explicit triangulation of $\CP^n$ is known for $n \geq 4$. |
| title | Some $\ZZ_3^n$-equivariant triangulations of $\CP^n$ |
| topic | Geometric Topology 05E18, 57Q15 |
| url | https://arxiv.org/abs/1405.2568 |