  The theory of measured foliations which is discussed in PartI(hep-th/9901040)
in connection with train tracks and meanders is shown to be related to the
theory of Jenkins-Strebel quadratic differentials by Hubbard and Masur (Acta
Math.Vol.142,221(1979)). Use of quadratic differentials not only provides an
adequate description of defects and textures in liquid crystals but also is
ideally suited for study of 2+1 classical gravity which was initiated in the
seminal paper by Deser, Jackiw and 't Hooft (Ann.Phys.Vol.152,220(1984)). In
this paper not only their results are reproduced but, in addition, many new
results are obtained. In particular, using the results of Rivin
(Ann.Math.Vol.139,553(1994)) the restriction on the total mass of the 2+1
Universe is removed. It is shown that the masses can have only discrete values
and, moreover, the theoretically obtained sum rules forbid the existence of
some of these values. The dynamics of 2+1 gravity which is associated with the
dynamics of train tracks is being reinterpreted in terms of the emerging
hyperbolic 3-manifolds. The existence of knots and links associated with
complements of these 3-manifolds is highly nontrivial and requires careful
proofs. The paper provides a concise introduction into this topic. A brief
discussion of connections with related physical problems, e.g.string theory,
classical and quantum billiards, dynamics of fracture, protein folding, etc. is
also provided.
