论文标题
圆锥形SL（3）泡沫
Conical SL(3) foams
论文作者
论文摘要
在无定向的SL（3）泡沫理论中，奇异顶点是二维复合物的通用奇异性。奇异的顶点在四面体的一个骨骼上具有同型圆锥的邻域，被视为两球上的三价图。在本文中，我们考虑了具有奇异顶点的泡沫，邻居在更一般的平面三价图上同型圆锥形。这些图在其kempe等效性泰特着色类别上受到适当的条件，并包括十二面体图。在对原始同源性理论的这种修改中，很简单地表明与十二面体图相关的模块没有等级60，这对于原始的无定向的SL（3）泡沫理论来说仍然是一个空旷的问题。
In the unoriented SL(3) foam theory, singular vertices are generic singularities of two-dimensional complexes. Singular vertices have neighbourhoods homeomorphic to cones over the one-skeleton of the tetrahedron, viewed as a trivalent graph on the two-sphere. In this paper we consider foams with singular vertices with neighbourhoods homeomorphic to cones over more general planar trivalent graphs. These graphs are subject to suitable conditions on their Kempe equivalence Tait coloring classes and include the dodecahedron graph. In this modification of the original homology theory it is straightforward to show that modules associated to the dodecahedron graph are free of rank 60, which is still an open problem for the original unoriented SL(3) foam theory.
