Properties of bordism classes of framed submanifolds of Fredholm structure (Q1387273)

Framed submanifolds of a Fredholm structure on a Banach manifold and their bordism groups have first been introduced by K. Elworthy and A. Tromba in order to define the degree of Fredholm mappings of positive index. They were later also used by V. G. Zvyagin and N. M. Ratiner to extend the degree theory to wider classes of mappings and to solutions of nonlinear differential equations. The present article studies the properties of bordism classes of framed submanifolds of a Fredholm structure on a Banach manifold. The results are formulated in three theorems which use a finite-dimensional approximation assumption.