Fold maps and immersions from the viewpoint of cobordism

Details Fold maps and immersions from the viewpoint of cobordism Fold maps and immersions from the viewpoint of cobordism

2007-05-18

arxiv.org/abs/0705.2731v2

Pacific J. Math. 239 (2009), 317-342.

Mathematics

Geometric Topology

revised, 16 pages, 1 figure

Scientific paper

We obtain complete geometric invariants of cobordism classes of oriented simple fold maps of (n+1)-dimensional manifolds into an n-dimensional manifold N in terms of immersions with prescribed normal bundles. We compute that this cobordism 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 group of the infinite dimensional projective space. 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 by natural homomorphisms between cobordism groups of immersions. We also compute the ranks of the oriented (right-left) bordism groups of simple fold maps.

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