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.
Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.
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 -