Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 24 min ago
PreprintCC BY-NC-ND 4.0HAL

Pseudo-Anosov flows and the geometry of Anosov-like group actions

  • Thomas Barthelmé
  • Kathryn Mann
  • Neige Paulet
  • Abdul Zalloum
Open at sourcePDFCite

Abstract

Anosov-like actions are group actions on R^2 generalizing the actions of 3-manifold groups on the orbit spaces of pseuso-Anosov flows. We show that any such action induces an isometric action on a Gromov hyperbolic metric space. When the flow (or plane) is not R-covered, we show this action has elements that are weakly properly discontinuous and deduce in the flows setting that elements of the 3-manifold group that do not represent a periodic orbit of the flow are generic for any word metric coming from a finite generating set. We also give a number of other results for Anosov-like group actions on bifoliated planes from a geometric group theory perspective.

Related

  1. Finiteness of Anosov and pseudo-Anosov flows on hyperbolic 3-manifolds
    David Gabai, Lily Qiao Li
    arXivPreprintarXiv licenceFull textDynamical systemsGeometry & topologyarXiv
  2. From Markovian actions to Anosov flows
    François Béguin, Ioannis Iakovoglou
    arXivPreprintCC BY 4.0Full textDynamical systemsarXiv
  3. Equidistribution of currents under Anosov group actions
    Nguyen-Bac Dang, Michael Kapovich, Mikhail Lyubich +1
    HALPreprintLicence not statedGeneral mathematicsHAL
  4. Endperiodic maps via pseudo-Anosov flows
    Michael P. Landry, Yair N. Minsky, Samuel J. Taylor
    Geometry & TopologyPeer-reviewedCC BY16 citedMathematical physicsOpenAlex
  5. Drilling veering triangulations with applications to pseudo-Anosov flows
    Anna Parlak, Henry Segerman
    arXivPreprintarXiv licenceFull textDynamical systemsGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{barthelme2026pseudoanosov,
  title = {{Pseudo-Anosov flows and the geometry of Anosov-like group actions}},
  author = {Thomas Barthelmé and Kathryn Mann and Neige Paulet and Abdul Zalloum},
  howpublished = {HAL},
  year = {2026},
  month = may,
  eprint = {2605.12837},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05837434v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Pseudo-Anosov flows and the geometry of Anosov-like group actions
AU  - Thomas Barthelmé
AU  - Kathryn Mann
AU  - Neige Paulet
AU  - Abdul Zalloum
PY  - 2026
DA  - 2026/05/13
PB  - HAL
UR  - https://hal.science/hal-05837434v1
AB  - Anosov-like actions are group actions on R^2 generalizing the actions of 3-manifold groups on the orbit spaces of pseuso-Anosov flows. We show that any such action induces an isometric action on a Gromov hyperbolic metric space. When the flow (or plane) is not R-covered, we show this action has elements that are weakly properly discontinuous and deduce in the flows setting that elements of the 3-manifold group that do not represent a periodic orbit of the flow are generic for any word metric coming from a finite generating set. We also give a number of other results for Anosov-like group actions on bifoliated planes from a geometric group theory perspective.
ER  -