2008/06/10 by David Shea Vela–Vick, Vela-Vick, David Shea · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #57M27 #57R58 #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.0806.1729
openalex publication_date 2008/06/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Consider a transverse knot which is the binding of an open book for the ambient contact manifold. In this paper, we show that the transverse invariants defined by Lisca, Ozsvath, Stipsicz, and Szabo (LOSS) are nonvanishing for such transverse knots. This is true regardless of whether or not the ambient contact structure is tight. We also prove a vanishing theorem for LOSS's Legendrian and transverse invariants. As a corollary, we show that if (T,π) is an open book with connected binding, then the complement of T has no Giroux torsion.