Floer homology and right-veering monodromy
-
John A. Baldwin
,
Yi Ni
Abstract
We prove that the knot Floer complex of a fibered knot detects whether the monodromy of its fibration is right-veering. In particular, this leads to a purely knot Floer-theoretic characterization of tight contact structures, by the work of Honda–Kazez–Matić. Our proof makes use of the relationship between the Heegaard Floer homology of mapping tori and the symplectic Floer homology of area-preserving surface diffeomorphisms. We describe applications of this work to Dehn surgeries and taut foliations.
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1952707
Award Identifier / Grant number: DMS-181190
Funding statement: J. A. Baldwin was supported by NSF FRG Grant DMS-1952707, Y. Ni was supported by NSF Grant DMS-181190.
Acknowledgements
We thank Andy Cotton-Clay, Nathan Dunfield, Matt Hedden, Ying Hu, Siddhi Krishna, Tye Lidman, Rachel Roberts, and Shea Vela-Vick for helpful correspondence. We particularly thank Siddhi for pointing out Corollary 1.9, and for first introducing us to the question posed in [15, Question 8.2]. We are also grateful to the referee for their helpful feedback on the initial version of this paper.
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Geometric main conjectures in function fields
- Noncompact self-shrinkers for mean curvature flow with arbitrary genus
- K-stability of Casagrande–Druel varieties
- Geometry at infinity of the space of Kähler potentials and asymptotic properties of filtrations
- The Nash problem for torus actions of complexity one
- Min-max theory for capillary surfaces
- Floer homology and right-veering monodromy
- The fourth moment of the Hurwitz zeta function
Articles in the same Issue
- Frontmatter
- Geometric main conjectures in function fields
- Noncompact self-shrinkers for mean curvature flow with arbitrary genus
- K-stability of Casagrande–Druel varieties
- Geometry at infinity of the space of Kähler potentials and asymptotic properties of filtrations
- The Nash problem for torus actions of complexity one
- Min-max theory for capillary surfaces
- Floer homology and right-veering monodromy
- The fourth moment of the Hurwitz zeta function
