### 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.

Original language | English |
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Pages (from-to) | 3825-3838 |

Number of pages | 14 |

Journal | Transactions of the American Mathematical Society |

Volume | 355 |

Issue number | 9 |

DOIs | |

Publication status | Published - Jan 1 2003 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*355*(9), 3825-3838. https://doi.org/10.1090/S0002-9947-03-03345-2

**Self-intersection class for singularities and its application to fold maps.** / Ohmoto, Toru; Saeki, Osamu; Sakuma, Kazuhiro.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 355, no. 9, pp. 3825-3838. https://doi.org/10.1090/S0002-9947-03-03345-2

}

TY - JOUR

T1 - Self-intersection class for singularities and its application to fold maps

AU - Ohmoto, Toru

AU - Saeki, Osamu

AU - Sakuma, Kazuhiro

PY - 2003/1/1

Y1 - 2003/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0042363657&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042363657&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-03-03345-2

DO - 10.1090/S0002-9947-03-03345-2

M3 - Article

AN - SCOPUS:0042363657

VL - 355

SP - 3825

EP - 3838

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 9

ER -