### Abstract

Let (M, N) be a manifold pair, where M is a closed 3-dimensional manifold and N is a closed 2-dimensional submanifold of M. In this paper, we first classify singular fibers of C^{∞} stable maps of (M, N) into surfaces. Then, we compute the cohomology groups of the associated universal complex of singular fibers, and obtain certain cobordism invariants for Morse functions on manifold pairs (M′, N′), where M′ is a closed surface and N′ is a closed 1-dimensional submanifold of M′. We also give the 2-colored versions of all these results, when the submanifold separates the ambient manifold into two parts.

Original language | English |
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Title of host publication | Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3 |

Editors | Jawad Snoussi, Raimundo Nonato Araujo dos Santos, Marcelo J. Saia, David Mond, Aurelio Menegon Neto |

Publisher | Springer New York LLC |

Pages | 259-294 |

Number of pages | 36 |

ISBN (Print) | 9783319736389 |

DOIs | |

Publication status | Published - Jan 1 2018 |

Event | 2nd Brazil-Mexico Meeting on Singularity and 3rd Northeastern Brazilian Meeting on Singularities, BMMS 2/NBMS 3 2015 - Salvador, Brazil Duration: Jul 13 2015 → Jul 17 2015 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 222 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Other

Other | 2nd Brazil-Mexico Meeting on Singularity and 3rd Northeastern Brazilian Meeting on Singularities, BMMS 2/NBMS 3 2015 |
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Country | Brazil |

City | Salvador |

Period | 7/13/15 → 7/17/15 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3*(pp. 259-294). (Springer Proceedings in Mathematics and Statistics; Vol. 222). Springer New York LLC. https://doi.org/10.1007/978-3-319-73639-6_8

**Singular fibers of stable maps of manifold pairs and their applications.** / Saeki, Osamu; Yamamoto, Takahiro.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3.*Springer Proceedings in Mathematics and Statistics, vol. 222, Springer New York LLC, pp. 259-294, 2nd Brazil-Mexico Meeting on Singularity and 3rd Northeastern Brazilian Meeting on Singularities, BMMS 2/NBMS 3 2015, Salvador, Brazil, 7/13/15. https://doi.org/10.1007/978-3-319-73639-6_8

}

TY - GEN

T1 - Singular fibers of stable maps of manifold pairs and their applications

AU - Saeki, Osamu

AU - Yamamoto, Takahiro

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Let (M, N) be a manifold pair, where M is a closed 3-dimensional manifold and N is a closed 2-dimensional submanifold of M. In this paper, we first classify singular fibers of C∞ stable maps of (M, N) into surfaces. Then, we compute the cohomology groups of the associated universal complex of singular fibers, and obtain certain cobordism invariants for Morse functions on manifold pairs (M′, N′), where M′ is a closed surface and N′ is a closed 1-dimensional submanifold of M′. We also give the 2-colored versions of all these results, when the submanifold separates the ambient manifold into two parts.

AB - Let (M, N) be a manifold pair, where M is a closed 3-dimensional manifold and N is a closed 2-dimensional submanifold of M. In this paper, we first classify singular fibers of C∞ stable maps of (M, N) into surfaces. Then, we compute the cohomology groups of the associated universal complex of singular fibers, and obtain certain cobordism invariants for Morse functions on manifold pairs (M′, N′), where M′ is a closed surface and N′ is a closed 1-dimensional submanifold of M′. We also give the 2-colored versions of all these results, when the submanifold separates the ambient manifold into two parts.

UR - http://www.scopus.com/inward/record.url?scp=85044444357&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044444357&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-73639-6_8

DO - 10.1007/978-3-319-73639-6_8

M3 - Conference contribution

AN - SCOPUS:85044444357

SN - 9783319736389

T3 - Springer Proceedings in Mathematics and Statistics

SP - 259

EP - 294

BT - Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3

A2 - Snoussi, Jawad

A2 - Araujo dos Santos, Raimundo Nonato

A2 - Saia, Marcelo J.

A2 - Mond, David

A2 - Menegon Neto, Aurelio

PB - Springer New York LLC

ER -