Singular fibers of stable maps of manifold pairs and their applications

Osamu Saeki, Takahiro Yamamoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationSingularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3
EditorsJawad Snoussi, Raimundo Nonato Araujo dos Santos, Marcelo J. Saia, David Mond, Aurelio Menegon Neto
PublisherSpringer New York LLC
Pages259-294
Number of pages36
ISBN (Print)9783319736389
DOIs
Publication statusPublished - Jan 1 2018
Event2nd Brazil-Mexico Meeting on Singularity and 3rd Northeastern Brazilian Meeting on Singularities, BMMS 2/NBMS 3 2015 - Salvador, Brazil
Duration: Jul 13 2015Jul 17 2015

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume222
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

Other2nd Brazil-Mexico Meeting on Singularity and 3rd Northeastern Brazilian Meeting on Singularities, BMMS 2/NBMS 3 2015
CountryBrazil
CitySalvador
Period7/13/157/17/15

Fingerprint

Stable Map
Fiber
Submanifolds
Closed
Morse Function
Cobordism
Cohomology of Groups
Classify
Invariant

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Saeki, O., & Yamamoto, T. (2018). Singular fibers of stable maps of manifold pairs and their applications. In J. Snoussi, R. N. Araujo dos Santos, M. J. Saia, D. Mond, & A. Menegon Neto (Eds.), 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.

Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3. ed. / Jawad Snoussi; Raimundo Nonato Araujo dos Santos; Marcelo J. Saia; David Mond; Aurelio Menegon Neto. Springer New York LLC, 2018. p. 259-294 (Springer Proceedings in Mathematics and Statistics; Vol. 222).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Saeki, O & Yamamoto, T 2018, Singular fibers of stable maps of manifold pairs and their applications. in J Snoussi, RN Araujo dos Santos, MJ Saia, D Mond & A Menegon Neto (eds), 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
Saeki O, Yamamoto T. Singular fibers of stable maps of manifold pairs and their applications. In Snoussi J, Araujo dos Santos RN, Saia MJ, Mond D, Menegon Neto A, editors, Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3. Springer New York LLC. 2018. p. 259-294. (Springer Proceedings in Mathematics and Statistics). https://doi.org/10.1007/978-3-319-73639-6_8
Saeki, Osamu ; Yamamoto, Takahiro. / Singular fibers of stable maps of manifold pairs and their applications. Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3. editor / Jawad Snoussi ; Raimundo Nonato Araujo dos Santos ; Marcelo J. Saia ; David Mond ; Aurelio Menegon Neto. Springer New York LLC, 2018. pp. 259-294 (Springer Proceedings in Mathematics and Statistics).
@inproceedings{b75c9347b2554845b81a5a9b678500d9,
title = "Singular fibers of stable maps of manifold pairs and their applications",
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.",
author = "Osamu Saeki and Takahiro Yamamoto",
year = "2018",
month = "1",
day = "1",
doi = "10.1007/978-3-319-73639-6_8",
language = "English",
isbn = "9783319736389",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer New York LLC",
pages = "259--294",
editor = "Jawad Snoussi and {Araujo dos Santos}, {Raimundo Nonato} and Saia, {Marcelo J.} and David Mond and {Menegon Neto}, Aurelio",
booktitle = "Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3",

}

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

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 -