从四重简单分支覆盖表示重构Turaev--Viro不变量
Reconstructing Turaev-Viro Invariants from Four-Fold Simple Branched Covering Presentations
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中文总结 AI 辅助
本文从对换标记的链环图构造有限状态和，将闭3-流形表示为四重简单分支覆盖，证明该状态和等于其SU(2)型Turaev--Viro不变量。
中文摘要 AI 辅助
我们从由对换标记的链环图构造有限状态和。该图将闭3-流形表示为四重简单分支覆盖，且该状态和等于该流形的SU(2)型Turaev--Viro不变量。对于图的边及互补区域的每个可容许着色，将全局因子与通过对相容局部着色求和得到的交叉权重相结合，随后对所有图着色的这些乘积求和。该公式通过组装逐交叉局部三角剖分并匹配两个状态和来证明。
英文摘要
We construct a finite state sum from a link diagram labelled by transpositions. The diagram presents a closed 3-manifold as a four-fold simple branched cover, and the state sum equals the SU(2)-type Turaev-Viro invariant of that manifold. For each admissible colouring of the diagram's edges and complementary regions, a global factor is combined with crossing weights obtained by summing over compatible local colourings. We then sum these products over all diagram colourings. The formula is proved by assembling crossing-wise local triangulations and matching the two state sums.
