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
References
Publication
Received: 18 May 2012
Revised: 16 January 2013
Accepted: 26 January 2013
Published: 17 May 2013
Authors
Boldizsár Kalmár
Alfréd Rényi Institute of Mathematics
Hungarian Academy of Sciences
Realtanoda U. 13–15
1053 Budapest
Hungary
András I Stipsicz
Alfréd Rényi Institute of Mathematics
Hungarian Academy of Sciences
Realtanoda U. 13–15
1053 Budapest
Hungary
http://www.renyi.hu/~stipsicz