Department of Mathematics2024-11-092011978-0-8218-5235-42324-707XN/Ahttps://hdl.handle.net/20.500.14288/13535Recently, Honda, Kazez and Matic described an adapted partial open book decomposition of a compact contact 3-manifold with convex boundary by generalizing the work of Giroux in the closed case. They also implicitly established a one-to-one correspondence between isomorphism classes of partial open book decompositions modulo positive stabilization and isomorphism classes of compact contact 3-manifolds with convex boundary. In this expository article we explicate the relative version of Giroux correspondence.MathematicsConference proceeding3036967000062982