Geometry & Topology

Singular fibers of stable maps and signatures of 4–manifolds

Osamu Saeki and Takahiro Yamamoto

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799711

Digital Object Identifier
doi:10.2140/gt.2006.10.359

Mathematical Reviews number (MathSciNet)
MR2224462

Zentralblatt MATH identifier
1107.57019

Subjects
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

Keywords
stable map singular fiber chiral fiber signature universal complex bordism

Citation

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. https://projecteuclid.org/euclid.gt/1513799711


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