Floer homology and right-veering monodromy
- Creators
- Baldwin, John A.1
-
Ni, Yi2
- Sivek, Steven3
-
1.
Boston College
-
2.
California Institute of Technology
-
3.
Imperial College London
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.
Copyright and License
© 2024 Walter de Gruyter GmbH, Berlin/Boston.
Acknowledgement
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.
Funding
J. A. Baldwin was supported by NSF FRG Grant DMS-1952707, Y. Ni was supported by NSF Grant DMS-181190.
Additional details
- National Science Foundation
- DMS-1952707
- National Science Foundation
- DMS-181190
- Publication Status
- Published