## Journal of the Mathematical Society of Japan

### Classification of singular fibres of stable maps of 4-manifolds into 3-manifolds and its applications

Takahiro YAMAMOTO

#### Abstract

In this paper we classify the singular fibres of stable maps of closed (possibly non-orientable) 4-manifolds into 3-manifolds up to the $C^{\infty}$ equivalence. Furthermore, we obtain several results on the co-existence of the singular fibres of such maps. As a consequence, we show that under certain conditions, the Euler number of the source 4-manifold has the same parity as the total number of certain singular fibres. This generalises Saeki's result in the orientable case.

#### Article information

Source
J. Math. Soc. Japan, Volume 58, Number 3 (2006), 721-742.

Dates
First available in Project Euclid: 23 August 2006

https://projecteuclid.org/euclid.jmsj/1156342035

Digital Object Identifier
doi:10.2969/jmsj/1156342035

Mathematical Reviews number (MathSciNet)
MR2254408

Zentralblatt MATH identifier
1105.57027

#### Citation

YAMAMOTO, Takahiro. Classification of singular fibres of stable maps of 4-manifolds into 3-manifolds and its applications. J. Math. Soc. Japan 58 (2006), no. 3, 721--742. doi:10.2969/jmsj/1156342035. https://projecteuclid.org/euclid.jmsj/1156342035

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