Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 16, Number 3 (2016), 1379-1402.
Singular fibers of stable maps of $3$–manifolds with boundary into surfaces and their applications
We first classify singular fibers of proper stable maps of –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.
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
Permanent link to this document
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
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