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,,7, via surgery on nullhomologous tori embedded in the standard manifolds 2#k¯2, k = 2,,7.

Keywords
$4$–manifold, Seiberg–Witten invariant
Mathematical Subject Classification 2010
Primary: 57R55
Secondary: 57R57, 14J26, 53D05
References
Publication
Received: 8 November 2010
Accepted: 17 March 2011
Published: 3 June 2011
Authors
Ronald Fintushel
Department of Mathematics
Michigan State University
East Lansing MI 48824
USA
http://www.math.msu.edu/~ronfint/
Ronald J Stern
Department of Mathematics
University of California, Irvine
Irvine CA 92697-3875
USA
http://math.uciedu/~rstern/