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

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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 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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1156342035

Digital Object Identifier
doi:10.2969/jmsj/1156342035

Mathematical Reviews number (MathSciNet)
MR2254408

Zentralblatt MATH identifier
1105.57027

Subjects
Primary: 57R45: Singularities of differentiable mappings
Secondary: 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx]

Keywords
stable map singular fibre Euler number two colour decomposition

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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