Local geometry of symplectic divisors with applications to contact torus bundles
Tian-Jun Li, Jie Min
TL;DR
This paper investigates the contact geometry of symplectic divisors, demonstrating invariance under certain modifications and constructing open book decompositions to analyze contact torus bundles.
Contribution
It introduces invariance results for contact structures under blow-ups and blow-downs and constructs open book decompositions for boundary analysis.
Findings
Contact structure invariance under toric and interior blow-ups/downs
Construction of open book decompositions for divisor boundaries
Application to universally tight contact structures of torus bundles
Abstract
In this note we study the contact geometry of symplectic divisors. We show the contact structure induced on the boundary of a divisor neighborhood is invariant under toric and interior blow-ups and blow-downs. We also construct an open book decomposition on the boundary of a concave divisor neighborhood and apply it to the study of universally tight contact structures of contact torus bundles.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology