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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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

stable map singular fiber manifold with boundary cobordism


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.

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