Cocycle rigidity of partially hyperbolic abelian actions with almost rank one factors

TL;DR

This paper advances the understanding of cocycle rigidity in partially hyperbolic abelian actions, especially those with rank one factors, by developing new methods to analyze cycle structures and prove vanishing results.

Contribution

It extends cocycle rigidity results to actions with rank one factors in the universal cover using novel arguments and analysis of cycle structures.

Findings

Established cocycle rigidity for actions with rank one factors

Developed new techniques for analyzing cycle structures

Proved vanishing results using the periodic cycle functional

Abstract

We extend the recent progress on the cocycle rigidity of partially hyperbolic homogeneous abelian actions to the setting with rank 1 factors in the universal cover. The method of proof relies on the periodic cycle functional and analysis of the cycle structure, but uses a new argument to give vanishing.