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arXiv · 2602.08514

A note on cocycles in $\mathbb{T}\times SO(3)$

Nikolaos Karaliolios
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Abstract

This short note studies $C^{\infty}$-smooth cocycles in $\mathbb{T}\times SO(3)$ that have $0$ degree and are non-homotopic to constants. The study picks up from where the author's PhD thesis left the subject, and shows that, under a relevant and full measure arithmetic condition, such cocycles can be conjugated to a simple model. Moreover, under the same arithmetic condition, the cocycle can be conjugated arbitrarily close to constant cocycles by a $2$-periodic conjugation.

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Nikolaos Karaliolios. 2026-02-09. A note on cocycles in $\mathbb{T}\times SO(3)$. https://arxiv.org/abs/2602.08514

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