Journal of the Mathematical Society of Japan

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


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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

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

First available in Project Euclid: 23 August 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

stable map singular fibre Euler number two colour decomposition


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.

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