This text presents a new perspective on pseudo-Anosov flows in 3-manifolds, suggesting significant simplifications in understanding topological dynamics.
In this text we (re)-tell the theory of pseudo-Anosov flows on 3-manifolds with the orbit space as the central character; via a streamlined framework called { Anosov-like group actions}. This brings a simplified and unified perspective, and allows for the import of tools from 1- and 2-dimensional topological dynamics. In so doing, we are able to give a relatively efficient presentation (or re-presentation) of foundational results in the field which appeared over several decades and many papers. We hope that the reader, whether a beginning or more advanced topologist or dynamicist, finds this a welcoming invitation to the rich theory of pseudo-Anosov flows.
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Barthelmé et al. (2025) studied this question.