  We construct using relatively basic techniques a spectral sequence for exact
Lagrangians in cotangent bundles similar to the one constructed by Fukaya,
Seidel, and Smith. That spectral sequence was used to prove that exact relative
spin Lagrangians in simply connected cotangent bundles with vanishing Maslov
class are homology equivalent to the base (a similar result was also obtained
by Nadler). The ideas in that paper were extended by Abouzaid who proved that
vanishing Maslov class alone implies homotopy equivalence.
  In this paper we present a short proof of the fact that any exact Lagrangian
with vanishing Maslov class is homology equivalent to the base and that the
induced map on fundamental groups is an isomorphism. When the fundamental group
of the base is pro-finite this implies homotopy equivalence.

Symplectic Geometry