2022/06/15 by Côme Dattin, Dattin, Côme
Mathematics · Medicine · #53D42 (Primary) 53D25 (Secondary) #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2206.07782
openalex publication_date 2022/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We apply the conormal construction to a hyperbolic knot K ⊂ S3, and study the sutured contact manifold (V, ξ) obtained by taking the complement of a standard neighbourhood of the unit conormal \LaK ⊂ (ST^*S3, ξst). We show that the sutured Legendrian contact homology of a unit fiber \La0, with its product structure, is a complete invariant of the knot (up to mirror). This can also be seen as the computation of the homology of the fiber in ST^* S3, stopped at \LaK. Our main tool is, for any submanifold N ⊂ M, an explicit relationship between the complement of a unit conormal \LaN, and the unit bundle of M ∖ N.