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

TL;DR

This paper establishes bounds on the spectral sequence's degeneration page for locally free isometric actions of abelian Lie groups, with examples confirming sharpness and potential applications to harmonic forms.

Contribution

It provides the first explicit bounds on the spectral sequence's degeneration page for these actions and demonstrates their sharpness through examples.

Findings

Bounds on the spectral sequence degeneration page are sharp.

Examples confirm the bounds are optimal.

Potential application to harmonic forms is discussed.

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.