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Singular fibers of stable maps of $3$–manifolds with boundary into surfaces and their applications

Osamu Saeki and Takahiro Yamamoto

Algebraic & Geometric Topology 16 (2016) 1379–1402
Abstract

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.

Keywords
stable map, singular fiber, manifold with boundary, cobordism
Mathematical Subject Classification 2010
Primary: 57R45
Secondary: 57R35, 57R90, 58K15, 58K65
References
Publication
Received: 26 May 2014
Revised: 18 June 2015
Accepted: 21 September 2015
Published: 1 July 2016
Authors
Osamu Saeki
Institute of Mathematics for Industry
Kyushu University
Motooka 744
Nishi-ku
Fukuoka 819-0395
Japan
Takahiro Yamamoto
Faculty of Engineering
Kyushu Sangyo University
3-1 Matsukadai 2-chome
Higashi-ku
Fukuoka 813-8503
Japan