  The paper concerns area preserving homeomorphisms of surfaces that are
isotopic to the identity. The purpose of the paper is to find a maximal
identity isotopy such that we can give a fine descriptions of the dynamics of
its transverse foliation. We will define a kind of identity isotopies:
torsion-low isotopies. In particular, when $f$ is a diffeomorphism with
finitely many fixed points such that every fixed point is not degenerate, an
identity isotopy $I$ of $f$ is torsion-low if and only if for every point $z$
fixed along the isotopy, the (real) rotation number $\rho(I,z)$, which is well
defined when one blows-up $f$ at $z$, is contained in $(-1,1)$. We will prove
the existence of torsion-low maximal identity isotopies, and we will deduce the
local dynamics of the transverse foliations of any torsion-low maximal isotopy
near any isolated singularity.
