局部自由等距李群作用的谱序

IF 0.4 3区数学 Q4 MATHEMATICS

Transformation Groups Pub Date : 2024-03-21 DOI:10.1007/s00031-024-09855-2

Paweł Raźny

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引用次数: 0

摘要

我们提出了自由等距李代数作用（进而是局部自由等距李群作用）的谱序列，它将流形的德拉姆同调与李代数同调和基本同调（直观上是轨道空间的同调）联系起来。在发展这个序列的过程中，我们引入了具有此类作用的流形的德拉姆同调的新描述，它似乎非常适合这个问题和类似问题。最后，我们提供了一些简单的应用，将王长精确序列推广到低码维的李代数作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Spectral Sequence for Locally Free Isometric Lie Group Actions

We present a spectral sequence for free isometric Lie algebra actions (and consequently locally free isometric Lie group actions) which relates the de Rham cohomology of the manifold with the Lie algebra cohomology and basic cohomology (intuitively the cohomology of the orbit space). In the process of developing this sequence, we introduce a new description of the de Rham cohomology of manifolds with such actions which appears to be well suited to this and similar problems. Finally, we provide some simple applications generalizing the Wang long exact sequence to Lie algebra actions of low codimension.

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来源期刊

Transformation Groups 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

100

审稿时长

9 months

期刊介绍： Transformation Groups will only accept research articles containing new results, complete Proofs, and an abstract. Topics include: Lie groups and Lie algebras; Lie transformation groups and holomorphic transformation groups; Algebraic groups; Invariant theory; Geometry and topology of homogeneous spaces; Discrete subgroups of Lie groups; Quantum groups and enveloping algebras; Group aspects of conformal field theory; Kac-Moody groups and algebras; Lie supergroups and superalgebras.