Steven Frankel
Announcements
I am helping to organize the St. Louis Topology Conference in May 2024. The topic is Flows and Foliations on 3-manifolds. Registration is open, and funding is available for students and early-career researchers.
Research
I am interested in geometric topology and dynamics, especially in combination: 3-manifolds, foliations, and hyperbolic geometry, quasigeodesic and pseudo-Anosov flows, partially hyperbolic diffeomorphisms, generalized pseudo-Anosov maps, groups acting on circles and trees, etc.
You can watch short talks about quasigeodesic flows here and here.
Publications
- Quasigeodesic flows and Mobius-like groups,
J. Diff. Geom. 93 (2013), no. 3, 401-429
[PDF, arXiv]
- Quasigeodesic flows from infinity,
PhD thesis, University of Cambridge (2013)
[PDF]
- Quasigeodesic flows and sphere-filling curves,
Geom. Topol. 19 (2015), no. 3, 1249-1262
[PDF, arXiv]
- Coarse hyperbolicity and closed orbits for quasigeodesic flows,
Ann. of Math. (2) 188 (2018), no. 1, 1-48
[PDF, arXiv]
- Research announcement: Partially hyperbolic diffeomorphisms homotopic to the identity on 3-manifolds (with T. Barthelme, S. Fenley, and R. Potrie),
2018 MATRIX Annals. Eds. D.R. Wood, J. de Gier, C.E. Praeger, T. Tao. Springer International Publishing, 2020.
[PDF, arXiv]
- Dynamical incoherence for a large class of partially hyperbolic diffeomorphisms (with T. Barthelme, S. Fenley, and R. Potrie),
Ergod. Theory Dyn. Syst. 41 (2021), no. 11, 3227-3243
[PDF, arXiv]
- Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part I: The dynamically coherent case (with T. Barthelme, S. Fenley, and R. Potrie),
to appear in Ann. Sci. Éc. Norm. Supér.
[arXiv]
- Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part II: Branching foliations (with T. Barthelme, S. Fenley, and R. Potrie),
Geom. Topol. 27 (2023), no. 8, 3095-3181
[arXiv]
- From veering triangulations to link spaces and back again (with S. Schleimer and H. Segerman),
submitted
[arXiv]
- Orbit equivalences of pseudo-Anosov flows (with T. Barthelme and K. Mann),
submitted
[arXiv]
- From quasigeodesic to pseudo-Anosov flows,
preprint available upon request