  In a previous paper we classified the homotopy classes of proper Fredholm
maps from an infinite dimensional Hilbert manifold to its model space in terms
of a suitable version of framed cobordism. We explicitly computed these
homotopy classes for non-positive index. In this paper we compute the homotopy
classes of proper Fredholm maps of index one from a simply connected Hilbert
manifold to its model space. This classification uses a new numerical invariant
for proper Fredholm maps of index one.
