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NON-COMPLEX SYMPLECTIC 4-MANIFOLDS WITH $\lowercase{b}_{2}^+ =1$

Published online by Cambridge University Press:  02 February 2004

JONGIL PARK
JONGIL PARK
Affiliation:
Department of Mathematics, Konkuk University, 1 Hwayang-dong, Kwangjin-gu, Seoul 143-701, Korea jipark@konkuk.ac.kr
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Abstract

Simply connected closed symplectic 4-manifolds with $b_{2}^+ \,{=}\,1$ and $K^2 \,{=}\,0$ are investigated. As a result, it is confirmed that most of homotopy elliptic surfaces $\{E(1)_{K} \,{|}\,K\, \mathrm{is\, a\, fibred\, knot}$ in $S^3\}$ constructed by R. Fintushel and R. Stern in Invent. Math. 134 (1998) 363–400 are simply connected closed minimal symplectic 4-manifolds that do not admit a complex structure.This work was supported by grant No. R14-2002-007-01002-0 from KOSEF.

Keywords

57R1757R57 (primary)14J26 (secondary)

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Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 2 , March 2004 , pp. 231 - 240
Copyright
© The London Mathematical Society 2004

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