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We obtain complete geometric invariants of cobordism classes of orientedsimple fold maps of (n+1)-dimensional manifolds into an n-dimensional manifoldN in terms of immersions with prescribed normal bundles. We compute that thiscobordism group of simple fold maps is isomorphic to the direct sum of the(n-1)th stable homotopy group of spheres and the (n-1)th stable homotopy groupof the infinite dimensional projective space. By using geometric invariantsdefined in the author's earlier works, we also describe the natural map of thesimple fold cobordism group to the fold cobordism group by naturalhomomorphisms between cobordism groups of immersions. We also compute the ranksof the oriented (right-left) bordism groups of simple fold maps.

Fold maps and immersions from the viewpoint of cobordism