Volume 7, issue 4 (2007)

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Reverse engineering small 4–manifolds

Ronald Fintushel, B Doug Park and Ronald J Stern

Algebraic & Geometric Topology 7 (2007) 2103–2116
 arXiv: math.GT/0701846
Abstract

We introduce a general procedure called ‘reverse engineering’ that can be used to construct infinite families of smooth $4$–manifolds in a given homeomorphism type. As one of the applications of this technique, we produce an infinite family of pairwise nondiffeomorphic $4$–manifolds homeomorphic to ${ℂℙ}^{2}#\phantom{\rule{0.3em}{0ex}}3{\overline{ℂℙ}}^{2}$.

Keywords
4–manifolds, Seiberg–Witten invariants
Mathematical Subject Classification 2000
Primary: 57R57, 57R57, 57R55
Secondary: 14J26, 53D05