Here, S is a surface , h is the monodromy of the abstract open book, and K is the fibered link that makes up the binding of the OB. More precisely, the Heegard decomposition is made of the three manifold we get by :i ) Doing the mapping torus of S by h ii) Gluing solid tori about the binding K. Is this just gluing, say $ H_1:=S imes [0,1/2)$ to $H_2:=S imes[1/2,1] $ with monodromy $h$ as the g