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Peer-reviewedCC BY-NC 4.0Communications of the American Mathematical Society

Reconstructing flows from the orbit space

  • Thomas Barthelmé
  • Sergio Fenley
  • Kathryn Mann
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Abstract

We give some simple conditions under which a group acting on a bifoliated plane comes from the induced action of a pseudo-Anosov flow on its orbit space. An application of the strategy is a less technical proof of a result of Barbot that the induced action of an Anosov flow on its orbit space uniquely determines the flow up to orbit equivalence. In another application, we recover an expansive flow on a 3-manifold from the action of a group on a loom space as defined by Schleimer and Segerman.

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Cite

BibTeXRIS
BibTeX
@article{barthelme2026reconstructing,
  title = {{Reconstructing flows from the orbit space}},
  author = {Thomas Barthelmé and Sergio Fenley and Kathryn Mann},
  journal = {Communications of the American Mathematical Society},
  year = {2026},
  month = oct,
  doi = {10.1090/cams/81},
  url = {https://hal.science/hal-05838021v1},
  note = {CC BY-NC 4.0},
}
RIS
TY  - JOUR
TI  - Reconstructing flows from the orbit space
AU  - Thomas Barthelmé
AU  - Sergio Fenley
AU  - Kathryn Mann
PY  - 2026
DA  - 2026/10/24
JO  - Communications of the American Mathematical Society
DO  - 10.1090/cams/81
UR  - https://hal.science/hal-05838021v1
AB  - We give some simple conditions under which a group acting on a bifoliated plane comes from the induced action of a pseudo-Anosov flow on its orbit space. An application of the strategy is a less technical proof of a result of Barbot that the induced action of an Anosov flow on its orbit space uniquely determines the flow up to orbit equivalence. In another application, we recover an expansive flow on a 3-manifold from the action of a group on a loom space as defined by Schleimer and Segerman.
SN  - 2692-3688
ER  -