基本阴影链环长积分填充的Chen-Yang体积猜想
The Chen-Yang volume conjecture for long integral fillings of fundamental shadow links
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中文总结 AI 辅助
本文证明了基本阴影链环外部空间的所有足够长整数Dehn填充满足Chen-Yang体积猜想，通过分析Turaev-Viro和Witten-Reshetikhin-Turaev不变量的渐近行为恢复双曲体积并确定前导系数。
中文摘要 AI 辅助
我们证明了任意固定的带标记基本阴影链环外部空间的所有足够长的整数Dehn填充的Chen-Yang体积猜想。对于每个固定的填充，其$SO(3)$ Turaev-Viro不变量的指数增长沿着完整的奇数层级序列恢复其双曲体积。填充系数可以具有混合符号和不相关的量级。我们还建立了带符号的$SO(3)$ Witten-Reshetikhin-Turaev不变量的完整渐近展开，并明确地用伴随Reidemeister挠率确定了绝对前导系数。填充核心上的固定偶数颜色恢复了几何和乐群的字符。关键困难在于带符号手术和中的抵消。我们的主要分析工具将精确反射对称性从连续模型转移到有限量子和中。我们将误差控制在幸存贡献的指数尺度以下。我们还将该方法应用于限制在中心颜色上的单边状态和。主导贡献相互抵消，对于每个足够大的固定块数，我们确定了较小的幸存指数增长率及其非零前导系数。
英文摘要
We prove the Chen--Yang volume conjecture for all sufficiently long integral Dehn fillings of any fixed marked fundamental shadow-link exterior. For each fixed filling, the exponential growth of its $SO(3)$ Turaev--Viro invariants recovers its hyperbolic volume along the full sequence of odd levels. The filling coefficients may have mixed signs and unrelated magnitudes. We also establish a complete asymptotic expansion of the signed $SO(3)$ Witten--Reshetikhin--Turaev invariant and identify the absolute leading coefficient explicitly in terms of adjoint Reidemeister torsion. Fixed even colors on the filling cores recover characters of the geometric holonomy. The key difficulty is cancellation in the signed surgery sum. Our main analytic tool transfers an exact reflection symmetry from a continuous model to the finite quantum sums. We control the error below the exponential scale of the surviving contribution. We also apply the method to a one-edge state sum restricted to central colors. The dominant contributions cancel, and for each sufficiently large fixed number of blocks we determine the smaller surviving exponential rate and its nonzero leading coefficient.
发表机构
- Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京国际数学研究中心）
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