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A Spectral Sequence for Locally Free Isometric Lie Group Actions

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Abstract

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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Acknowledgements

The author would like to thank Professor Martin Saralegui-Aranguren for his insightful remarks and sharing details of his work on related topics.

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  1. Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University in Cracow, Kraków, Poland

    Paweł Raźny

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  1. Paweł Raźny
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Correspondence to Paweł Raźny.

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Raźny, P. A Spectral Sequence for Locally Free Isometric Lie Group Actions. Transformation Groups (2024). https://doi.org/10.1007/s00031-024-09855-2

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