Journal of the Mathematical Society of Japan

Cobordism group of Morse functions on surfaces

Kazuichi IKEGAMI and Osamu SAEKI

Full-text: Open access

Abstract

We define the cobordism group of Morse functions on manifolds and show that it is an infinite cyclic group for dimension two in the oriented case. We also give an explicit Morse function which gives a generator of the group.

Article information

Source
J. Math. Soc. Japan, Volume 55, Number 4 (2003), 1081-1094.

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191418765

Digital Object Identifier
doi:10.2969/jmsj/1191418765

Mathematical Reviews number (MathSciNet)
MR2003761

Zentralblatt MATH identifier
1046.57020

Subjects
Primary: 57R45: Singularities of differentiable mappings
Secondary: 57R75: O- and SO-cobordism

Keywords
Morse function cobordism fold singularity Reeb graph Stein factorization

Citation

IKEGAMI, Kazuichi; SAEKI, Osamu. Cobordism group of Morse functions on surfaces. J. Math. Soc. Japan 55 (2003), no. 4, 1081--1094. doi:10.2969/jmsj/1191418765. https://projecteuclid.org/euclid.jmsj/1191418765


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