Singular fibers of stable maps and signatures of 4–manifolds

Saeki, Osamu; Yamamoto, Takahiro

doi:10.2140/gt.2006.10.359

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Singular fibers of stable maps and signatures of 4–manifolds

Osamu Saeki and Takahiro Yamamoto

Geometry & Topology 10 (2006) 359–399

DOI: 10.2140/gt.2006.10.359

arXiv: 0902.4576

Abstract

We show that for a $C^{\infty}$ 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.

Keywords

stable map, singular fiber, chiral fiber, signature, universal complex, bordism

Mathematical Subject Classification 2000

Primary: 57R45

Secondary: 57N13, 58K30, 58K15

References

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Publication

Received: 8 October 2004

Accepted: 12 January 2006

Published: 7 April 2006

Proposed: Yasha Eliashberg

Seconded: Shigeyuki Morita, Rob Kirby

Authors

Osamu Saeki
Faculty of Mathematics Kyushu University Hakozaki Fukuoka 812-8581 Japan
http://www.math.kyushu-u.ac.jp/~saeki/
Takahiro Yamamoto
Department of Mathematics Hokkaido University Sapporo 060-0810 Japan

Volume 10, issue 1 (2006)