Tight contact structures on some bounded Seifert manifolds with minimal convex boundary

2011/11/08 by Fan Ding, Ding, Fan, Youlin Li +3
Mathematics · #53D10 #57M50 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1111.1900

openalex publication_date 2011/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify positive tight contact structures, up to isotopy fixing the boundary, on the manifolds N=M(D²; r₁, r₂) with minimal convex boundary of slope s and Giroux torsion 0 along ∂ N, where r₁,r₂∈ (0,1)∩ℚ, in the following cases: (1) s∈(-∞, 0)∪[2, +∞); (2) s∈[0, 1) and r₁,r₂∈ [1/2,1); (3) s∈[1, 2) and r₁,r₂∈(0,1/2); (4) s=∞ and r₁=r₂=1/2. We also classify positive tight contact structures, up to isotopy fixing the boundary, on M(D²;1/2,1/2) with minimal convex boundary of arbitrary slope and Giroux torsion greater than 0 along the boundary.

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