发表机构
Heinrich-Heine-Universität Düsseldorf（杜塞尔多夫海因里希·海涅大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文回顾Rumin复形与解析接触挠率，利用表示论及Boothby-Wang构造，将对称接触流形的接触挠率计算化为调和形式与Dolbeault上同调，并推广至等变情形以确定孤立不动点处的等变接触挠率。
AI 中文摘要
我们回顾了Rumin复形和接触流形的解析接触挠率的定义。随后，我们计算对称接触流形的接触挠率。为此，我们使用了相关算子和微分形式空间的表示论描述。我们对对称接触流形接触挠率的计算依赖于Rumin最近的一个结果，该结果将问题归结为调和形式。遵循Boothby和Wang的构造，所考虑的接触流形是Kähler流形上$S^1$-主丛的全空间。这使我们能够将调和形式解释为底Kähler流形上某个全纯线丛系数的Dolbeault上同调，从而通过使用复几何的结果简化计算。此外，我们将Rumin的结果推广到等变情形，并利用前述考虑，确定孤立不动点情形下的等变接触挠率。
英文摘要
We review the definitions of the Rumin complex and analytic contact torsion for contact manifolds. We then compute the contact torsion for symmetric contact manifolds. To this end, we use a representation-theoretic description of the relevant operators and spaces of differential forms. Our computation of the contact torsion for symmetric contact manifolds relies on a recent result by Rumin that reduces the problem to harmonic forms. Following a construction by Boothby and Wang, the contact manifolds under consideration are total spaces of $S^1$-principal bundles over Kähler manifolds. This allows us to interpret the harmonic forms as Dolbeault cohomology with coefficients in a certain holomorphic line bundle of the base Kähler manifold, thereby simplifying the computation by allowing us to use results from complex geometry. Furthermore, we generalise Rumin's result to the equivariant case and, using the previous considerations, determine the equivariant contact torsion for the case of isolated fixed points.
Comments32 pages
