All 2–dimensional links in 4–space live inside a universal 3–dimensional polyhedron.
All 2–dimensional links in 4–space live inside a universal 3–dimensional polyhedron.
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4 空间中的所有 2 维链接都存在于通用 3 维多面体内。
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
V. Kurlin
中科院分区：
文献类型：
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作者：
C. Kearton;V. Kurlin
六面体书是两个四面体沿着共同的面粘合而成的一维骨架的圆锥体。万能三维多面体UP是线段和六元书的产物。我们证明了4维空间中的任何闭2维曲面都与UP中的曲面同位。证明是基于4维空间中的曲面用标记图表示的，即3维空间中具有双交点的链环。我们构造了一个有限表示的半群，它的中心元素唯一地编码了所有的2维曲面的保纯类。57Q45、57Q35、57Q37
The hexabasic book is the cone of the 1‐dimensional skeleton of the union of two tetrahedra glued along a common face. The universal 3‐dimensional polyhedron UP is the product of a segment and the hexabasic book. We show that any closed 2‐dimensional surface in 4‐space is isotopic to a surface in UP. The proof is based on a representation of surfaces in 4‐space by marked graphs, links with double intersections in 3‐space. We construct a finitely presented semigroup whose central elements uniquely encode all isotopy classes of 2‐dimensional surfaces. 57Q45, 57Q35, 57Q37