Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 58, Number 3 (2006), 721-742.
Classification of singular fibres of stable maps of 4-manifolds into 3-manifolds and its applications
In this paper we classify the singular fibres of stable maps of closed (possibly non-orientable) 4-manifolds into 3-manifolds up to the 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.
J. Math. Soc. Japan, Volume 58, Number 3 (2006), 721-742.
First available in Project Euclid: 23 August 2006
Permanent link to this document
Digital Object Identifier
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]
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