We show that if a partially hyperbolic diffeomorphism of a Seifert manifold induces a map in the base which has a pseudo-Anosov component then it cannot be dynamically coherent. This extends [C. Bonatti, A. Gogolev, A. Hammerlindl and R. Potrie. Anomalous partially hyperbolic diffeomorphisms III: Abundance and incoherence. Geom. Topol., to appear] to the whole isotopy class. We relate the techniques to the study of certain partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds performed in [T. Barthelmé, S. Fenley, S. Frankel and R. Potrie. Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, part I: The dynamically coherent case. Preprint, 2019, arXiv:1908.06227; Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, part II: Branching foliations. Preprint, 2020, arXiv: 2008.04871]. The appendix reviews some consequences of the Nielsen–Thurston classification of surface homeomorphisms for the dynamics of lifts of such maps to the universal cover.

中文翻译：

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一大类部分双曲微分同胚的动态不相干性

我们表明，如果 Seifert 流形的部分双曲微分同胚在基中诱导出具有伪阿诺索夫分量的映射，则它不能是动态相干的。这扩展了 [C. Bonatti、A. Gogolev、A. Hammerlindl 和 R. Potrie。异常部分双曲微分同胚III：丰度和不连贯。几何。白杨。, 出现] 到整个同位素类。我们将这些技术与在 [T. Barthelmé、S. Fenley、S. Frankel 和 R. Potrie。部分双曲微分同胚与第 3 维中的恒等式同伦，第一部分：动态相干情况。预印本, 2019, arXiv:1908.06227; 部分双曲微分同胚于第 3 维中的同一性，第二部分：分枝叶。预印本, 2020, arXiv: 2008.04871]。附录回顾了 Nielsen-Thurston 表面同胚分类的一些结果，这些结果对于此类地图提升到普遍覆盖的动力学。