Remarks on the Topology of Folds

Kikuchi, Shigeki; Saeki, Osamu

doi:10.2307/2160817

Proceedings of the American Mathematical Society

1995

DOI: 10.2307/2160817

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Remarks on the Topology of Folds

Shigeki Kikuchi¹,

Osamu Saeki²

Abstract: Abstract. We give some necessary conditions for a closed manifold to admit a smooth map into an Euclidean space with only fold singular points.

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2003

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Cited by 2 publications

References 5 publications

(8 reference statements)

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Self-intersection class for singularities and its application to fold maps

Ohmoto

Saeki

Sakuma

2003

Trans. Amer. Math. Soc.

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Abstract. Let f : M → N be a generic smooth map with corank one singularities between manifolds, and let S(f ) be the singular point set of f . We define the self-intersection class I(S(f )) ∈ H * (M ; Z) of S(f ) using an incident class introduced by Rimányi but with twisted coefficients, and give a formula for I(S(f )) in terms of characteristic classes of the manifolds. We then apply the formula to the existence problem of fold maps.

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Self-intersection class for singularities and its application to fold maps

Ohmoto

Saeki

Sakuma

2003

Trans. Amer. Math. Soc.

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The Chess conjecture

Sadykov

2003

Algebr. Geom. Topol.

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Remarks on the Topology of Folds

Abstract: Abstract. We give some necessary conditions for a closed manifold to admit a smooth map into an Euclidean space with only fold singular points.

Cited by 2 publications

References 5 publications

Self-intersection class for singularities and its application to fold maps

Self-intersection class for singularities and its application to fold maps

The Chess conjecture

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