A characterization of $g_2$-minimal normal 3-pseudomanifolds with at most four singularities
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866915301839339520 |
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| author | Basak, Biplab Gupta, Raju Kumar Sarkar, Sourav |
| author_facet | Basak, Biplab Gupta, Raju Kumar Sarkar, Sourav |
| contents | Let $Δ$ be a $g_2$-minimal normal 3-pseudomanifold. A vertex in $Δ$ whose link is not a sphere is called a singular vertex. When $Δ$ contains at most two singular vertices, its combinatorial characterization is known [9]. In this article, we present a combinatorial characterization of such a $Δ$ when it has three singular vertices, including one $\mathbb{RP}^2$-singularity, or four singular vertices, including two $\mathbb{RP}^2$-singularities. In both cases, we prove that $Δ$ is obtained from a one-vertex suspension of a surface, and some boundary complexes of $4$-simplices by applying the combinatorial operations of types connected sums, vertex foldings, and edge foldings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2202_06582 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A characterization of $g_2$-minimal normal 3-pseudomanifolds with at most four singularities Basak, Biplab Gupta, Raju Kumar Sarkar, Sourav Combinatorics General Topology Primary 57Q05, Secondary 05E45, 51B10, 51E20, 52B70 Let $Δ$ be a $g_2$-minimal normal 3-pseudomanifold. A vertex in $Δ$ whose link is not a sphere is called a singular vertex. When $Δ$ contains at most two singular vertices, its combinatorial characterization is known [9]. In this article, we present a combinatorial characterization of such a $Δ$ when it has three singular vertices, including one $\mathbb{RP}^2$-singularity, or four singular vertices, including two $\mathbb{RP}^2$-singularities. In both cases, we prove that $Δ$ is obtained from a one-vertex suspension of a surface, and some boundary complexes of $4$-simplices by applying the combinatorial operations of types connected sums, vertex foldings, and edge foldings. |
| title | A characterization of $g_2$-minimal normal 3-pseudomanifolds with at most four singularities |
| topic | Combinatorics General Topology Primary 57Q05, Secondary 05E45, 51B10, 51E20, 52B70 |
| url | https://arxiv.org/abs/2202.06582 |