Invariants of Fold-maps via Stable Homotopy Groups

  • Yoshifumi Ando

    Yamaguchi University, Yamaguchi City, Japan


In the 2-jet space of smooth map germs with , we consider the subspace consisting of all 2-jets of regular germs and map germs with fold singularities. In this paper we determine the homotopy type of the space . Let and be smooth () manifolds of dimensions and . A smooth map is called a fold-map if has only fold singularities. We will prove that this homotopy type is very useful in finding invariants of fold-maps. For instance, by applying the homotopy principle for fold-maps in [An3] and [An4] we prove that if is odd and is connected, then there exists a surjection of the set of cobordism classes of fold-maps into to the stable homotopy group . Here, is the normal bundle of in and denote the canonical vector bundles of dimension over the grassman manifold . We also prove the oriented version.

Cite this article

Yoshifumi Ando, Invariants of Fold-maps via Stable Homotopy Groups. Publ. Res. Inst. Math. Sci. 38 (2002), no. 2, pp. 397–450

DOI 10.2977/PRIMS/1145476344