Geometry & Topology

Singular fibers of stable maps and signatures of 4–manifolds

Osamu Saeki and Takahiro Yamamoto

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We show that for a C stable map of an oriented 4–manifold into a 3–manifold, the algebraic number of singular fibers of a specific type coincides with the signature of the source 4–manifold.

Article information

Geom. Topol., Volume 10, Number 1 (2006), 359-399.

Received: 8 October 2004
Accepted: 12 January 2006
First available in Project Euclid: 20 December 2017

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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] 58K30: Global theory 58K15: Topological properties of mappings

stable map singular fiber chiral fiber signature universal complex bordism


Saeki, Osamu; Yamamoto, Takahiro. Singular fibers of stable maps and signatures of 4–manifolds. Geom. Topol. 10 (2006), no. 1, 359--399. doi:10.2140/gt.2006.10.359.

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