Speaker
Description
In this talk, we characterize normal $3$-pseudomanifolds $K$ with $g_2(K) \leq 4$. It is known that if a normal $3$-pseudomanifold $K$ with $g_2(K) \leq 4$ has no singular vertices, then it is a triangulated $3$-sphere. We first prove that a normal $3$-pseudomanifold $K$ with $g_2(K) \leq 4$ has at most two singular vertices. Subsequently, we show that if $K$ is not a triangulated $3$-sphere, it can be obtained from certain boundary complexes of $4$-simplices by a sequence of operations, including connected sums, edge expansions, and edge folding. Furthermore, we establish that such a $3$-pseudomanifold $K$ is a triangulation of the suspension of $\mathbb{RP}^2$. Additionally, by building upon the results of Walkup, we provide a reframed characterization of normal $3$-pseudomanifolds with no singular vertices for $g_2(K) \leq 9$
