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

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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