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

Abstract

In this paper, 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.

18 pages with 7 figures

References in corpus (2)

• Singular fibers of stable maps and signatures of 4-manifolds
• Cobordism of Morse functions on surfaces, the universal complex of singular fibers and their application to map germs

Cited by in corpus (1)

• Non-singular extensions of horizontal stable fold maps from surfaces to the plane