从11四面体普查的视角看3-流形在S^4中的嵌入
Embeddings of 3-manifolds in S^4 from the point of view of the 11-tetrahedron census
AI总结：
本文围绕3-流形能否光滑嵌入4-球面的问题，基于11四面体素闭3-流形普查筛选出149个候选流形开展研究，明确了其中部分流形的嵌入性结果，留下37个待解决情形。
摘要：
本文是关于3-流形嵌入问题的一组笔记。核心探讨的问题是“哪些3-流形可以光滑嵌入4-球面？”，研究范围限定在Burton/Martelli/Matveev/Petronio普查中由不超过11个四面体构建的素闭3-流形三角剖分集合。该普查共包含13766个流形，其中13400个为可定向流形。在这13400个可定向流形中，仅有149个具有双曲挠环绕结形式，因此是4-球面可嵌入性的候选对象。本文大部分内容聚焦于这149个流形的嵌入问题。目前已知其中41个可嵌入4-球面；在剩余流形中，有4个被构造出到同伦4-球面的嵌入；67个已知无法嵌入4-球面。最终仍有37个未解决情形，其中仅3个是几何流形（即具有平凡JSJ分解的流形）。
英文摘要：
This is a collection of notes on embedding problems for 3-manifolds. The main question explored is `which 3-manifolds embed smoothly in the 4-sphere?' The terrain of exploration is the Burton/Martelli/Matveev/Petronio census of triangulated prime closed 3-manifolds built from 11 or less tetrahedra. There are 13766 manifolds in the census, of which 13400 are orientable. Of the 13400 orientable manifolds, only 149 of them have hyperbolic torsion linking forms and are thus candidates for embedability in the 4-sphere. The majority of this paper is devoted to the embedding problem for these 149 manifolds. At present 41 are known to embed. Among the remaining manifolds, embeddings into homotopy 4-spheres are constructed for 4. 67 manifolds are known to not embed in the 4-sphere. This leaves 37 unresolved cases, of which only 3 are geometric manifolds i.e. having a trivial JSJ-decomposition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
