TY - JOUR
T1 - Singular fibers of stable maps of 3-manifolds with boundary into surfaces and their applications
AU - Saeki, Osamu
AU - Yamamoto, Takahiro
N1 - Funding Information:
The authors would like to express their sincere gratitude to Shigeo Takahashi, Daisuke Sakurai, Hsiang-Yun Wu, Keisuke Kikuchi and Hamish Carr for stimulating discussions and for posing interesting questions. The authors would also like to thank the referee for very important comments which drastically improved the presentation of the paper. The first author has been supported in part by JSPS KAKENHI Grant Number 23244008, 23654028, 25540041, 15K13438. The second author has been supported in part by JSPS KAKENHI Grant Number 23654028, 15K13438.
Publisher Copyright:
© 2016, Mathematical Sciences Publishers. All rights reserved.
PY - 2016/7/1
Y1 - 2016/7/1
N2 - We first classify singular fibers of proper C∞ stable maps of 3-dimensional manifolds with boundary 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 compact surfaces with boundary.
AB - We first classify singular fibers of proper C∞ stable maps of 3-dimensional manifolds with boundary 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 compact surfaces with boundary.
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U2 - 10.2140/agt.2016.16.1379
DO - 10.2140/agt.2016.16.1379
M3 - Article
AN - SCOPUS:84978933150
SN - 1472-2747
VL - 16
SP - 1379
EP - 1402
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
IS - 3
ER -