Every lens space that supports a non-free toric contact action has exactly one tight and two overtwisted contact structures up to contactomorphism, and all are concave boundaries of linear plumbings.
Introduction to Contact Topology Cambridge University Press (2009)
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Contact 3-manifolds that admit a non-free toric action
Every lens space that supports a non-free toric contact action has exactly one tight and two overtwisted contact structures up to contactomorphism, and all are concave boundaries of linear plumbings.