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# Classification of tight contact structures on some Seifert fibered manifolds: I

Mar 2023

We classify tight contact structures with zero Giroux torsion on some Seifertfibered manifolds with four exceptional fibers,$M=M(0;-q_1/p_1,-q_2/p_2,-q_3/p_3,-q_4/p_4)$ where $e_0\leq -4$ and $p_i, q_i\in \mathbb{Z}$ s.t., $p_i\geq 2$, $q_i\geq 1$. We get lower bound byconstructing contact structures by Legendrian surgery. We use convex surfacetheory to obtain the upper bound.

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