由Thurston多面体的纤维面索引的量子不变量
Quantum Invariants indexed by Fibered Faces of the Thurston Polytope
- California Institute of Technology（加州理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究有向链环的Gukov--Manolescu量子不变量，发现其多个级数与Melvin--Morton--Rozansky展开一致，并猜想由Alexander多项式单项式索引的级数对应Thurston范数球的纤维面，提供计算证据及首项和Dehn手术相关结果。
AI中文摘要：
我们研究有向链环的Gukov--Manolescu量子不变量。虽然该不变量在纽结情形下是单一级数，但我们发现链环具有多个这样的级数，每个级数与彩色Jones多项式的Melvin--Morton--Rozansky展开一致。我们证明收敛的倒置态和产生一族多元Gukov--Manolescu级数，由Alexander多项式的单项式索引。我们猜想这些单项式恰好对应于Thurston范数球的纤维面，并为这一对应关系提供了广泛的计算证据。此外，我们还建立了关于首项、相应的单变量不变量以及部分Dehn手术效应的进一步结果。
英文摘要：
We study the Gukov--Manolescu quantum invariant for oriented links. While this invariant is a single series in the knot case, we find that links admit multiple such series, each one consistent with the Melvin--Morton--Rozansky expansion of the colored Jones polynomials. We prove that convergent inverted state sums yield a family of multivariable Gukov--Manolescu series, indexed by monomials of the Alexander polynomial. We conjecture that these monomials correspond precisely to the fibered faces of the Thurston norm ball and provide extensive computational evidence for this correspondence. Further results concerning the leading term, the corresponding single-variable invariant, and the effect of partial Dehn surgery are also established.
