On a construction of pseudo-Anosov diffeomorphisms by sequences of train tracks (Q1891182)

Let \(M\) be a close orientable surface of genus \(\geq 2\). A train track \(\tau\) on \(M\) is a one-dimensional finite CW-complex embedded in \(M\) which is \(C^1\) (in certain sense) and no components of \(M \setminus \tau\) are 0,1,2-gons or annuli. It was known that pseudo-Anosov diffeomorphisms are representable by sequences of train tracks with some property. The author establishes the necessary and sufficient condition for a sequence of train tracks to be a representation of a pseudo-Anosov diffeomorphism.