A lamination L embedded in a
manifold M is an affine lamination if its lift L to the universal cover M of M is a
measured lamination and each covering translation multiplies the measure by a factor
given by a homomorphism, called the stretch homomorphism, from π1(M) to the
positive real numbers. There is a method for analyzing precisely the set of affine
laminations carried by a given branched manifold B embedded in M. The notion of
the “stretch factor” of an affine lamination 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.
Affine laminations occur commonly as essential 2-dimensional laminations in
3-manifolds. We shall describe some examples. In particular, we describe affine
essential laminations which represent classes in real 2-dimensional homology with
twisted coefficients.
