AFFINE LAMINATIONS AND THEIR STRETCH FACTORS

A lamination L embedded in a manifold M is an affine lamination if its lift L to the universal cover (M) over tilde of M is a measured lamin ation;and each covering translation multiplies the measure by a factor given by a homomorphism, called the stretch homomorphism, from pi(1)( M) to the positive real numbers. There is a method for analyzing preci sely the set of affine laminations carried by a given branched manifol d B embedded in M. The notion of the ''stretch factor'' of an affine l amination is a generalization of the notion of the stretch factor of a pseudo-Anosov map. The same method that serves to analyze the affine laminations carried by B also allows calculation of stretch factors. A ffine laminations occur commonly as essential 2-dimensional lamination s in 3-manifolds. We shall describe some examples. In particular, we d escribe affine essential laminations which represent classes in real 2 -dimensional homology with twisted coefficients.