Analytic torsion versus Reidemeister torsion on hyperbolic 3-manifolds with cusps
Analytic torsion versus Reidemeister torsion on hyperbolic 3-manifolds with cusps
复制标题
带尖点的双曲 3 流形上的解析扭转与 Reidemeister 扭转
DOI：
10.1007/s00209-014-1287-5
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发表时间：
2012
影响因子：
0.8
通讯作者：
J. Pfaff
中科院分区：
文献类型：
--
作者：
J. Pfaff
对于非紧的带尖点的双曲3-流形，我们证明了一个显式公式，该公式将$$SL }_2（\mathbb {C}）$$SL 2（C）的标准表示的偶对称幂的正则化解析挠率与相应的Reidemeister挠率联系起来.虽然解析挠率是流形的谱不变量，但雷德迈斯特挠率具有组合性质。我们的证明依赖于一个表达式的分析扭转的特殊价值Ruelle zeta函数以及最近的工作神父Menal费雷尔和琼波蒂。
For a non-compact hyperbolic 3-manifold with cusps we prove an explicit formula that relates the regularized analytic torsion associated to the even symmetric powers of the standard representation of $$\mathrm{SL }_2(\mathbb {C})$$SL2(C) to the corresponding Reidemeister torsion. While the analytic torsion is a spectral invariant of the manifold, the Reidemeister torsion is of combinatorial nature. Our proof rests on an expression of the analytic torsion in terms of special values of Ruelle zeta functions as well as on recent work of Pere Menal-Ferrer and Joan Porti.