On the properties of the cobordism group of stably-framed immersions in codimension k

Abstract

The notion „intermediate bordism group“, which was introduced by P. J. Eccles to investigate filtrations in stable homotopy group of spheres, is considered. А new notion „cobordism groups of stable-framed immersions“ is introduced. The classifying space for the new groups is constructed, ranks of the groups are calculated. Hopf invariants and the Kahn-Priddy homomorphism are generalized for cobordism groups of stable-framed immersions.