#### Volume 13, issue 3 (2013)

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Singular maps on exotic $4$–manifold pairs

### Boldizsár Kalmár and András I Stipsicz

Algebraic & Geometric Topology 13 (2013) 1709–1731
##### Abstract

We show examples of pairs of smooth, compact, homeomorphic $4$–manifolds, whose diffeomorphism types are distinguished by the topology of the singular sets of smooth stable maps defined on them. In this distinction we rely on results from Seiberg–Witten theory.

##### Keywords
$4$–manifold, smooth structure, stable map, genus function, Seiberg–Witten invariant
##### Mathematical Subject Classification 2010
Primary: 57R55
Secondary: 57R45, 57M50, 57R15