In page 13 of the paper:
It is stated that "An open book decomposition (S,h, K) , gives rise to a special Heegard decomposition of M ". 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 \times [0,1/2)$ to $H_2:=S \times[1/2,1] $ with monodromy $h$ as the gluing map?
Just curious as to any explanation/ref. of what this Heegard splitting associated to the open book (S,h,K) is.
Thanks for any explanations, refs.