TY - GEN

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

AU - Saeki, Osamu

AU - Yamamoto, Takahiro

N1 - Funding Information:
Acknowledgements The authors would like to thank the anonymous referee for some comments which improved the presentation of the paper. The first author has been supported in part by JSPS KAKENHI Grant Numbers JP23244008, JP23654028, JP25540041, JP15K13438, JP16H03936, JP16K13754, JP17H01090, JP17H06128. The second author has been supported in part by JSPS KAKENHI Grant Numbers JP23654028, JP15H03615, JP15K04880, JP15K13438, JP17H01090, JP17H06128.

PY - 2018

Y1 - 2018

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.

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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

T2 - 2nd Brazil-Mexico Meeting on Singularity and 3rd Northeastern Brazilian Meeting on Singularities, BMMS 2/NBMS 3 2015

Y2 - 13 July 2015 through 17 July 2015

ER -