  We classify the homotopy classes of proper Fredholm maps from an infinite
dimensional Hilbert manifold into its model space in terms of a suitable
version of framed cobordism. Our construction is an alternative approach to the
classification introduced by Elworthy and Tromba in 1970 and does not make use
of further structures on the ambient manifold, such as Fredholm structures. In
the special case of index zero, we obtain a complete classification involving
the Caccioppoli-Smale mod 2 degree and the absolute value of the oriented
degree.
