4维流形的三等分不变量是不可计算的
Trisection invariants of 4-manifolds are uncomputable
AI总结：
该研究证明了光滑4维流形的三等分亏格与Kirby-Thompson L-不变量不可计算，还解决了K3问题列表中问题4.116的第二部分，并证明了维数≥4的PL流形的PL多三等分亏格不可计算。
AI中文摘要：
我们证明了由三等分定义的光滑4维流形的两个不变量是不可计算的：三等分亏格和Kirby-Thompson L-不变量。也就是说，不存在以三角化的闭定向4维流形为输入并输出其中一个量的算法。关于L-不变量的结果解决了K3问题列表中问题4.116的第二部分。同样地，我们证明了维数至少为4的PL流形的PL多三等分亏格是不可计算的。
英文摘要：
We prove that two invariants of smooth 4-manifolds defined in terms of trisections are uncomputable: the trisection genus and the Kirby-Thompson L-invariant. That is, there does not exist an algorithm that takes as input a triangulated closed orientable 4-manifold and outputs one of these quantities. The result on the L-invariant resolves the second part of Problem 4.116 in the K3 problem list. In the same spirit, we show that the PL multisection genus of PL manifolds is uncomputable in dimensions at least four.
