Journal of Mathematics of Kyoto University

Stable homotopy groups of spheres and higher singularities

Yoshifumi Ando

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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

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250283004

Digital Object Identifier
doi:10.1215/kjm/1250283004

Mathematical Reviews number (MathSciNet)
MR2260821

Zentralblatt MATH identifier
1114.57033

Subjects
Primary: 57R45: Singularities of differentiable mappings
Secondary: 55Q45: Stable homotopy of spheres 57R90: Other types of cobordism [See also 55N22]

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


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