Rational blow-down along Wahl type plumbing trees of spheres

Michalogiorgaki, Maria

doi:10.2140/agt.2007.7.1327

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Rational blow-down along Wahl type plumbing trees of spheres

Maria Michalogiorgaki

Algebraic & Geometric Topology 7 (2007) 1327–1343

DOI: 10.2140/agt.2007.7.1327

arXiv: math.GT/0607608

Abstract

In this article, we construct smooth 4–manifolds homeomorphic but not diffeomorphic to ${ℂ ℙ}^{2} # k {\bar{ℂ ℙ}}^{2}$ , for $k \in {6, 7, 8, 9},$ using the technique of rational blow-down along Wahl type plumbing trees of spheres (see J Wahl, Smoothings of normal surface singularities, Topology 20 (1981) 219–246).

Keywords

exotic smooth 4–manifolds, Seiberg–Witten invariants, rational blow-down

Mathematical Subject Classification 2000

Primary: 57R55, 57R57

Secondary: 14J26, 53D05

References

Publication

Received: 11 October 2006

Revised: 16 April 2007

Accepted: 17 August 2007

Published: 24 September 2007

Authors

Maria Michalogiorgaki
Department of Mathematics Princeton University Fine Hall Washington Road Princeton NJ 08544 USA

Volume 7, issue 3 (2007)