SIGMA 22 (2026), 072, 18 pages      arXiv:2506.12422      https://doi.org/10.3842/SIGMA.2026.072

A Study of the Spectral Sequence for Locally Free Isometric Actions of Abelian Lie Groups

Paweł Raźny
Institute of Mathematics, Jagiellonian University in Cracow, ul. prof. Stanislawa Łojasiewicza 6, 30-348 Kraków, Poland

Received June 17, 2025, in final form July 27, 2026; Published online August 08, 2026

Abstract
We give an upper bound on the number of the page on which the spectral sequence corresponding to a locally free isometric action of an abelian Lie group degenerates. We give examples showing that these bounds are indeed sharp. Finally, we further justify the study of this sequence by exhibiting a potential application to the study of harmonic forms.

Key words: Lie group actions; Lie algebra actions; foliations; basic cohomology; isometries.

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