We obtain complete
geometric invariants of cobordism classes of oriented simple fold maps of
(n + 1)-dimensional manifolds into an n-dimensional manifold Nn in terms of
immersions with prescribed normal bundles. We compute that for Nn= ℝn the
cobordism group of simple fold maps is isomorphic to the direct sum of the (n− 1)-st
stable homotopy group of spheres and the (n − 1)-st stable homotopy group of the
space ℝP∞. By using geometric invariants defined in the author’s earlier works, we
also describe the natural map of the simple fold cobordism group to the fold
cobordism group in terms of natural homomorphisms between cobordism groups of
immersions. We also compute the ranks of the oriented bordism groups of simple fold
maps.
Keywords
fold singularity, immersion, cobordism, simple fold map,
stable homotopy group
