On the transverse invariant for bindings of open books

Details On the transverse invariant for bindings of open books On the transverse invariant for bindings of open books

2008-06-10

arxiv.org/abs/0806.1729v2

Mathematics

Symplectic Geometry

18 pages, 8 figures. The new version contains some minor updates and typo corrections

Scientific paper

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,\pi) is an open book with connected binding, then the complement of T has no Giroux torsion.

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