论文标题
$ g_2 \ leq4 $的正常$ 3 $ -PSEUDMONIFOLDS的表征
A characterization of normal $3$-pseudomanifolds with $g_2\leq4$
论文作者
论文摘要
我们用$ g_2 \ leq4 $表征了普通$ 3 $ -PSEUDOMANIFOLDS。我们知道，如果带有$ g_2 \ leq4 $的$ 3 $ -PSEUDMONIFOLD没有任何单数顶点，那么它是$ 3 $ -sphere。我们首先证明，带有$ g_2 \ leq4 $的普通$ 3 $ -Pseudomanifold最多具有两个单数顶点。然后，我们证明，使用$ g_2 \ leq 4 $的普通$ 3 $ -PSEUDMONIFOLD，这不是$ 3 $ -SPHERE，它是通过一系列连接的运营总和，边缘扩展和边缘折叠从某个边界获得的$ 4 $ simplices。此外，通过使用[17]，我们重新构架了$ g_2 \ leq 9 $的普通$ 3 $ -pseudomanifolds，当它没有单数顶点时。
We characterize normal $3$-pseudomanifolds with $g_2\leq4$. We know that if a $3$-pseudomanifold with $g_2\leq4$ does not have any singular vertices then it is a $3$-sphere. We first prove that a normal $3$-pseudomanifold with $g_2\leq4$ has at most two singular vertices. Then we prove that a normal $3$-pseudomanifold with $g_2 \leq 4$, which is not a $3$-sphere is obtained from some boundary of $4$-simplices by a sequence of operations connected sum, edge expansion and an edge folding. In addition, by using [17], we re-framed the characterization of normal $3$-pseudomanifolds with $g_2\leq 9$, when it has no singular vertices.
