Sergio Fenley
About
Sergio Fenley is a professor of mathematics at Florida State University. He obtained his Ph.D. from Princeton University in 1989, under the guidance of Professor William Thurston. He has worked primarily with foliations, Anosov flows, and pseudo-Anosov flows in dimension 3, analyzing the interaction between topology, geometry, and dynamics. More recently he is involved with codimension one Anosov flows in higher dimensions, and has recently disproved the Verjovsky's conjecture in dimension 4 (jointly with Kathryn Mann and Rafael Potrie). He also recently proved that most Anosov flows in hyperbolic 3-manifolds are quasigeodesic, and obtained a complete classification of partially hyperbolic diffeomorphisms in dimension 3 (jointly with Andy Hammerlindl and Rafael Potrie).
Anosov flows in dimension 3, and codimension one Anosov flows. Partially hyperbolic diffeomorphisms. Quasigeodesic properties of flows.
[1] Depth one foliations in hyperbolic 3-manifolds - Ph.D. thesis, Princeton University, 1989.
[2] Asymptotic properties of depth one foliations in hyperbolic 3-manifolds, Jour. Di . Geom. 36 (1992) 269-313.
[3] Quasi-isometric foliations, Topology 31 (1992) 667-676.
[4] Anosov flows in 3-manifolds, Ann. of Math 139 (1994) 79-115.
[5] Quasigeodesic Anosov flows and homotopic properties of flow lines, Jour. Di . Geom., 41 (1995) 479-514.
[6] One sided branching in Anosov foliations, Comm. Math. Helv., 70 (1995) 248-266.
[7] End periodic surface homeomorphisms and 3-manifolds, Math. Zeit. 224 (1997) 1-24.
[8] Incompressible tori transverse to Anosov flows in 3-manifolds, Erg. Th. Dyn. Sys. 17 (1997) 105-121.
[9] Homotopic indivisibility of closed orbits of 3-dimensional Anosov flows, Math. Zeit., 225 (1997) 289-294.
[10] Quasi-Fuchsian Seifert surfaces, Math. Zeit., 228 (1998) 221-227.
[11] The structure of branching in Anosov flows of 3-manifolds, Comm. Math. Helv., 73 (1998) 259-297.
[12] Local and global properties of limit sets of foliations of quasigeodesic Anosov flows, Trans.
A.M.S., 350 (1998) 3923-3941.
[13] Limit sets of foliations in hyperbolic 3-manifolds, Topology, 37 (1998) 875-894.
[14] Continuous extension of Anosov foliations in 3-manifolds with negatively curved fundamental group, Paci c Jour. Math. 186 (1999) 201-216.
[15] Surfaces transverse to pseudo-Anosov flows and virtual bers, Topology 38 (1999) 823-859.
[16] Foliations with good geometry, Journal A.M.S. 10 (1999) 619-676.
[17] (with Lee Mosher) Quasigeodesic flows in hyperbolic 3-manifolds, Topology 40 (2001) 503-537.
[18] Foliations, topology and geometry of 3-manifolds: R-covered foliations and transverse pseudo-Anosov flows, Comm. Math. Helv 77 (2002) 415-490.
[19] Pseudo-Anosov flows and incompressible tori, Geometriae Dedicata 99 (2003) 61-102.
[20] Regulating flows, topology of foliations and rigidity, Trans. A.M.S. 357 (2005) 4957-5000.
[21] Laminar free hyperbolic 3-manifolds, Comm. Math. Helv., 82 (2007) 247-321.
[22] Asymptotic geometry of foliations and pseudo-Anosov flows - a survey, Proceedings of Groups and Di eomorphisms conference, Advanced Studies in Pure Mathematics, vol 52, 2008, 1-20.
[23] Geometry of foliations and flows I: Almost transverse pseudo-Anosov flows and asymptotic behavior of foliations, Jour. Di . Geom., 81 (2009) 1-89.
[24] (with Renato Feres and Kamlesh Parwani) Harmonic functions on R-covered foliations and group actions on the circle, Erg. Th. Dyn. Sys., 29 (2009) 1141-1161.
[25] Ideal boundaries of pseudo-Anosov flows and uniform convergence groups, with connections and applications to large scale geometry, Geometry and Topology, 16 (2012) 1-110.
[26] Rigidity of pseudo-Anosov flows transverse to R-covered foliations, Comm. Math. Helv., 88 (2013) 643-676.
[27] (with Thierry Barbot) Pseudo-Anosov flows in toroidal manifolds, arxiv: math.GT/1007.0578, Geometry and Topology, 17 (2013) 1877-1954.
[28] (with Thomas Barthelme) Knot theory of R-covered Anosov flows: homotopy versus isotopy of closed orbits, arxiv: math.DS/1208.6487, Journal of Topology, 7 (2014) 677-696.
[29] (with Thierry Barbot) Classification and rigidity of totally periodic pseudo-Anosov flows in graph manifolds, arxiv: math. GT/1211.7327, Erg. Th. Dyn. Sys., 35 (2015) 1681-1722.
[30] Diversified homotopic behavior of closed orbits of some R-covered flows, arxiv: math.GT/1403.03 Erg. Th. Dyn. Sys., 36 (2016) 767-780.
[31] Quasigeodesic pseudo-Anosov flows in hyperbolic 3-manifolds and connections with large scale geometry, arxiv: math. GT/1405.4542, Advances in Math. 303 (2016) 192-278.
[32] (with Thomas Barthelme) Counting periodic orbits of Anosov flows in free homotopy classes, arxiv: math. 1505.07999, Comm. Math. Helv. 92 (2017) 641-714.
[33] (with Thomas Barthelme, Steven Frankel and Rafael Potrie) Partially hyperbolic diffeomor-phisms homotopic to the identity on 3-manifolds, 2018 Matrix Annals (2020) 341-357.
[34] (with John Cantwell and Larry Conlon) Endperiodic automorphisms of surfaces and folia-tions, arxiv: math.1006.4525, Ergodic Theory and Dynamical Systems, 41 (2021) 66-212.
[35] (with Thierry Barbot), Free Seifert pieces of pseudo-Anosov flows, Geometry and Topology, arxiv: math.1512.06341, Geometry and Topology 25 (2021) 1331-1440.
[36] (with Rafael Potrie) Minimality of the action on the universal circle of uniform foliations, math.arxiv: 2001.05522, Groups, Geom. Dyn. 15 (2021) 1489-1521.
[37] (with Thomas Barthelme, Steven Frankel and Rafael Potrie) Dynamical incoherence for a large class of partially hyperbolic diffeomorphisms, math.arxiv: 2002.10315, Erg. Th. Dyn. Sys. 41 (2021) 3227-3243.
[38] (with Rafael Potrie) Ergodicity of partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds, math.arxiv: 1809.02284, Adv. Math., Paper 108315, 45 pages (2022).
[39] R-covered foliations and transverse pseudo-Anosov flows in atoroidal pieces, math.arxiv: 2101.10984, Comm. Math. Helv. 98 (2023) 1-39.
[40] (with Thomas Barthelme, Steven Frankel and Rafael Potrie) Partially hyperbolic diffeo-morphisms homotopic to the identity in dimension 3, Part II, Branching foliations, math.arxiv: 2008.04871, Geom. Topol. 27 (2023) 3095-3181.
[41] (with Anindya Chanda) Leafwise quasigeodesic foliations in dimension three and the funnel property, math.arxiv: 2105.05430, Erg.Th.Dyn.Sys., 43 (2023) 2624-2650.
[42] (with Thomas Barthelme, Rafael Potrie) Collapsed Anosov flows and self orbit equivalences, math.arxiv: 2008.06547, Comm. Math. Helv. 98 (2023) 771-875.
[43] (with Thomas Barthelme, Steven Frankel and Rafael Potrie) Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part I, The dynamically coherent case, math.arxiv: 1908.06227, Ann. Ecole Normale Sup. 57 (2024) 293-349.
[44] (with Rafael Potrie) Accessibility and ergodicity for collapsed Anosov flows, math.arxiv: 2103.14630, Amer. J. Math. 146 (2024) 1339-1359.
[45] (with Rafael Potrie) Partial hyperbolicity and pseudo-Anosov dynamics, math.arxiv: 2102.02156, Geom. and Func. Anal. 34 (2024) 409-485.
[46] (with Anindya Chanda) New classes of quasigeodesic flows in 3-manifolds, math.arxiv: 2211.12679, Erg. Th. Dyn. Sys. 45 (2025) 2095-2131.
[47] (with Thomas Barthelme and Katryn Mann) Anosov flows with the same periodic orbits, math.arxiv: 2309.02098, Jour. Modern Dyn. 21 (2025) 361-400.
[48] (with Rafael Potrie) Intersection of transverse foliations in 3-manifolds: Hausdor leafspace implies leafwise quasigeodesic, math.arxiv: 2310.05176, Crelle (Jour. fur die reine and angewandte Mathematick) 822 (2025) 1-48.
[49] (with Rafael Potrie) Transverse minimal foliations on unit tangent bundles and applications, Pac. Jour. Math. 343 (2026) 39-118.
[50] Non R-covered Anosov flows in hyperbolic 3-manifolds are quasigeodesic, Geom. Func. Anal., 36 (2026) 412-508, math.arxiv: 2210.09238.
[50] (with Thierry Barbot) Orbital equivalence of nite coverings of geodesic flows, to appear in Advances in Mathematics, math.arxiv: 2205.02495, 21 pages.
[52] (with Thierry Barbot and Rafael Potrie) On transverse R-covered minimal foliations, to appear in Alg. Geom. Topol., math.arxiv: 2501.14489, 42 pages.
[53] (with Thomas Barthelme and Kathryn Mann) Reconstructing flows from the orbit space, to appear in Comm. A.M.S., math.arxiv: 2509.01594, 31 pages.
[54] (with Rafael Potrie) Partially hyperbolic di eomorphisms, ergodicity, and transverse foliations, submitted, math.arxiv: 2510.15176, 57 pages.
[55] (with Thomas Barthelme and Rafael Potrie) appendix to Topological invariance of Liouville structures for taut foliations and Anosov flows, submitted, math.arxiv: 2510.15325.
[56] (with Kathryn Mann and Rafael Potrie) Exotice codimension one Anosov flows, submitted, math.arxiv: 2605.25082, 21 pages.
[57] (with Michael Landry and Sam Taylor) Simultaneous universal circles and continuous extension, math.arxiv: 2607.05703.
[58] (with Tali Pinsky and Mario Shannon) Hyperbolicity of complements of orbits of Anosov flows, math.arxiv: 2607.28139.
Fall 2026: Calculus 2 (2 sections), Differential Topology