Volume 11, issue 3 (2011)

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Pinwheels and nullhomologous surgery on $4$–manifolds with $b^+=1$

Ronald Fintushel and Ronald J Stern

Algebraic & Geometric Topology 11 (2011) 1649–1699
Abstract

We present a method for finding embedded nullhomologous tori in standard $4$–manifolds which can be utilized to change their smooth structure. As an application, we show how to obtain infinite families of simply connected smooth $4$–manifolds with ${b}^{+}=1$ and ${b}^{-}=2,\dots ,7$, via surgery on nullhomologous tori embedded in the standard manifolds ${ℂ‘ℙ}^{2}#k\phantom{\rule{0.3em}{0ex}}{\overline{ℂ‘ℙ}}^{2}$, $k=2,\dots ,7$.

Keywords
$4$–manifold, Seiberg–Witten invariant
Mathematical Subject Classification 2010
Primary: 57R55
Secondary: 57R57, 14J26, 53D05