Volume 10, issue 1 (2006)

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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
 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