The 3D index of an ideal triangulation and angle structures
The 3D index of an ideal triangulation and angle structures
复制标题
理想三角测量和角度结构的 3D 索引
DOI：
10.1007/s11139-016-9771-7
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
S. Garoufalidis
中科院分区：
文献类型：
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作者：
S. Garoufalidis
三维Dimofte-Gaiotto-Gukov指标是三维流形上具有r个环面边界分支的理想三角剖分集合上的部分定义函数。对于一个固定的2 r整数元组，索引取具有整数系数的q-级数集合中的值。我们的目标是给出一个公理化定义的四面体指数和证明域的3D索引组成的一组理想的三角形，支持一个索引结构。后者是严格角结构的推广。我们还证明了3D索引在3-2步下是不变的，但在2-3步下不是一般不变的。
The 3D index of Dimofte–Gaiotto–Gukov is a partially defined function on the set of ideal triangulations of 3-manifolds with r tori boundary components. For a fixed 2r tuple of integers, the index takes values in the set of q-series with integer coefficients. Our goal is to give an axiomatic definition of the tetrahedron index and a proof that the domain of the 3D index consists precisely of the set of ideal triangulations that support an index structure. The latter is a generalization of a strict angle structure. We also prove that the 3D index is invariant under 3–2 moves, but not in general under 2–3 moves.