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

Saeki, Osamu; Yamamoto, Takahiro

doi:10.2140/agt.2016.16.1379

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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

DOI: 10.2140/agt.2016.16.1379

Abstract

We first classify singular fibers of proper $C^{\infty}$ 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

Volume 16, issue 3 (2016)