TITLE: Open book decompositions of $T^3$
QUESTION [5 upvotes]: Please pardon my ignorance on the subject of open books, I'm a noob.  I would like to know some explicit descriptions of open book decompositions of the three torus $T^3$.  Are there examples with connected binding?  
Is there a direct topological proof that shows that every 3-manifold admits an open book decomposition?  Ideally, such a proof might start with a Heegaard decomposition or a surgery description of a given 3-manifold, and then proceed to give an algorithm for converting this to an open book decomposition.  In such a case, I suppose I could then follow such a proof to answer my first question regarding $T^3$.

REPLY [4 votes]: As mentioned in a comment, Ken Baker has a nice visualization of an open book decomposition of $T^3$ due to Jeremy Van-Horn Morris. 

One way to get open book structures is to start with a fibered universal knot or link, and then pull back the open book structure from $S^3$ to a branched cover which is branched over that link. The Whitehead link, the Borromean rings, and the figure 8 knot are all fibered links that are known to be universal. 
In fact, every open book decomposition of a 3-manifold pulls back as a branched cover of $S^3$ of the standard open book decomposition of the unknot.