Algebraic & Geometric Topology

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

Osamu Saeki and Takahiro Yamamoto

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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.

Article information

Source
Algebr. Geom. Topol., Volume 16, Number 3 (2016), 1379-1402.

Dates
Received: 26 May 2014
Revised: 18 June 2015
Accepted: 21 September 2015
First available in Project Euclid: 28 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1511895850

Digital Object Identifier
doi:10.2140/agt.2016.16.1379

Mathematical Reviews number (MathSciNet)
MR3523043

Zentralblatt MATH identifier
1360.57034

Subjects
Primary: 57R45: Singularities of differentiable mappings
Secondary: 57R35: Differentiable mappings 57R90: Other types of cobordism [See also 55N22] 58K15: Topological properties of mappings 58K65: Topological invariants

Keywords
stable map singular fiber manifold with boundary cobordism

Citation

Saeki, Osamu; Yamamoto, Takahiro. Singular fibers of stable maps of $3$–manifolds with boundary into surfaces and their applications. Algebr. Geom. Topol. 16 (2016), no. 3, 1379--1402. doi:10.2140/agt.2016.16.1379. https://projecteuclid.org/euclid.agt/1511895850


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