2000 character limit reached
Obstructing Anosov flows on cusped 3-manifolds
Published 25 Mar 2024 in math.GT and math.DS | (2403.17060v1)
Abstract: Using results relating taut foliations and pseudo-Anosov flows, we find cusped hyperbolic 3-manifolds which are not the non-singular part of a pseudo-Anosov flow. In particular, we find the first examples of cusped hyperbolic 3-manifolds not admitting veering triangulations, confirming a conjecture of S. Schleimer.
- Ian Agol. Ideal triangulations of pseudo-Anosov mapping tori. In W. Li, L. Bartolini, J. Johnson, F.Luo, R. Myers, and J.H. Rubinstein, editors, Topology and Geometry in Dimension Three: Triangulations, Invariants, and Geometric Structures, volume 560 of Contemporary Mathematics. American Mathematical Society, 2011.
- Some smooth ergodic systems. Uspekhi matematicheskikh nauk, 22(5):103–167, 1967.
- Dynamics of veering triangulations: infinitesimal components of their flow graphs and applications. arXiv:2201.02706 to appear in Algebraic and Geometric Topology, 2022.
- Danny Calegari. Foliations and the Geometry of 3-Manifolds. Oxford Mathematical Monographs. Clarendon Press, 2007.
- SnapPy, a computer program for studying the geometry and topology of 3333-manifolds. Available at \urlhttp://snappy.computop.org (01/06/2023).
- Nathan Dunfield. Code and data to accompany “Floer homology, group orderability, and taut foliations of hyperbolic 3-manifolds” Harvard Dataverse https://doi.org/10.7910/dvn/lcyxpo.
- Nathan Dunfield. Floer homology, group orderability, and taut foliations of hyperbolic 3-manifolds. Geometry and Topology, 24(4):2075–2125, 2020.
- Tight contact structures and Anosov flows. Topology and its Applications, 124(2):211–219, 2002.
- Explicit angle structures for veering triangulations. Algebraic and Geometric Topology, 13(1):205–235, 2013.
- David Gabai. Taut foliations of 3-manifolds and suspensions of S1superscript𝑆1{S}^{1}italic_S start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT. Annales de l’institut Fourier, 42(1-2):193–208, 1992.
- A census of veering structures. \urlhttps://math.okstate.edu/people/segerman/veering.html 2024/02/18.
- Veering triangulations admit strict angle structures. Geometry and Topology, 15(4):2073–2089, 2011.
- Marc Lackenby. Word hyperbolic Dehn surgery. Inventiones Mathematicae, 140:243–282, 2000.
- Flows, growth rates, and the veering polynomial. Ergodic Theory and Dynamical Systems, 43(9):3026–3107, 2023.
- Sergei Petrovich Novikov. The topology of foliations. Trudy Moskovskogo matematicheskogo obshchestva, 14:248–278, 1965.
- Holomorphic disks and genus bounds. Geometry and Topology, 8(1):311–334, 2004.
- Anna Parlak. Veering triangulations and polynomial invariants of three-manifolds. PhD thesis, University of Warwick, 2021.
- Floer simple manifolds and L-space intervals. Advances in Mathematics, 322:738–805, 2017.
- Infinitely many hyperbolic 3-manifolds which contain no reebless foliation. Journal of the American Mathematical Society, 16(3):639–679, 2003.
- Saul Schleimer. The veering census. In ICERM talk slides, November 2019.
- The figure-eight knot has only one veering triangulation. In preparation.
- From veering triangulations to pseudo-Anosov flows and back again. In preparation.
- From veering triangulations to dynamics pairs. preprint https://arxiv.org/abs/2305.08799, 2023.
- From loom space to veering triangulations. Groups, Geometry, and Dynamics, 18(1):1–44, 2024.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.
