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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∞ 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

Primary: 57R45

Secondary: 57N13, 58K15, 58K30
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