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