## Journal of Mathematics of Kyoto University

### Stable homotopy groups of spheres and higher singularities

Yoshifumi Ando

#### Abstract

We will construct an isomorphism of the group of all cobordism classes of fold-maps of degree 0 of $n$-dimensional closed oriented manifolds to the $n$-sphere to the $n$-th stable homotopy group $\pi _{n}^{s}$ of spheres. As an application we will show that elements of $\pi _{n}^{s}$ are detected by higher singularities of certain maps in dimensions $n < 8$.

#### Article information

Source
J. Math. Kyoto Univ., Volume 46, Number 1 (2006), 147-165.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250283004

Digital Object Identifier
doi:10.1215/kjm/1250283004

Mathematical Reviews number (MathSciNet)
MR2260821

Zentralblatt MATH identifier
1114.57033

#### Citation

Ando, Yoshifumi. Stable homotopy groups of spheres and higher singularities. J. Math. Kyoto Univ. 46 (2006), no. 1, 147--165. doi:10.1215/kjm/1250283004. https://projecteuclid.org/euclid.kjm/1250283004