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

Fintushel, Ronald; Stern, Ronald J

doi:10.2140/agt.2011.11.1649

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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

DOI: 10.2140/agt.2011.11.1649

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 ${ℂ ‘ ℙ}^{2} # k {\bar{ℂ ‘ ℙ}}^{2}$ , $k = 2, \dots, 7$ .

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/

Volume 11, issue 3 (2011)