Volume 6, issue 2 (2006)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
Cobordism of Morse functions on surfaces, the universal complex of singular fibers and their application to map germs

Osamu Saeki

Algebraic & Geometric Topology 6 (2006) 539–572

arXiv: 0903.1733


We give a new and simple proof for the computation of the oriented and the unoriented fold cobordism groups of Morse functions on surfaces. We also compute similar cobordism groups of Morse functions based on simple stable maps of 3–manifolds into the plane. Furthermore, we show that certain cohomology classes associated with the universal complexes of singular fibers give complete invariants for all these cobordism groups. We also discuss invariants derived from hypercohomologies of the universal homology complexes of singular fibers. Finally, as an application of the theory of universal complexes of singular fibers, we show that for generic smooth map germs g: (3,0) (2,0) with 2 being oriented, the algebraic number of cusps appearing in a stable perturbation of g is a local topological invariant of g.

Morse function, cobordism, singular fiber, universal complex, simple stable map, hypercohomology, stable perturbation, map germ
Mathematical Subject Classification 2000
Primary: 57R45
Secondary: 57R75, 58K60, 58K65
Forward citations
Received: 22 September 2005
Accepted: 25 January 2006
Published: 7 April 2006
Osamu Saeki
Faculty of Mathematics
Kyushu University
Fukuoka 812-8581