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arXiv:2202.06582v3 Announce Type: replace
Abstract: Let $\Delta$ be a $g_2$-minimal normal 3-pseudomanifold. A vertex in $\Delta$ whose link is not a sphere is called a singular vertex. When $\Delta$ contains at most two singular vertices, its combinatorial characterization is known [9]. In this article, we present a combinatorial characterization of such a $\Delta$ 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 $\Delta$ 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.
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