论文标题
关于具有有限的载体的扁平矢量束的较高扭转不变的评论
A remark on the higher torsion invariants for flat vector bundles with finite holonomy
论文作者
论文摘要
我们表明，对于任何平坦的矢量捆绑包，Igusa-klein拓扑扭转和bismut-lott分析扭转都是等效的，其固体是$ \ mathrm {gl} _n（\ mathbb {q}）的有限亚组。我们的证明在表示理论中使用Artin的归纳定理将问题减少到琐碎的平面束的特殊情况下，这是Puchol，Zhu和第二作者的最新结果。使用Artin的归纳定理的想法出现在OHRT的论文中，就同一主题而言，我们目前的工作是一种改进。
We show that the Igusa-Klein topological torsion and the Bismut-Lott analytic torsion are equivalent for any flat vector bundle whose holonomy is a finite subgroup of $\mathrm{GL}_n(\mathbb{Q})$. Our proof uses Artin's induction theorem in representation theory to reduce the problem to the special case of trivial flat line bundles, which is a recent result of Puchol, Zhu and the second author. The idea of using Artin's induction theorem appeared in a paper of Ohrt on the same topic, of which our present work is an improvement.
