Remarks on higher type adjunction inequalities of 4-manifolds of non-simple type
Bull. Korean Math. Soc. 2002 Vol. 39, No. 3, 431-440
Printed September 1, 2002
Jin-Hong Kim
KAIST
Abstract : Recently P. Ozsv\' ath and Z. Szab\' o proved higher type adjunction inequalities for embedded surfaces in 4-manifolds of non-simple type. The aim of this short paper is to give a simple and direct proof of such higher type adjunction inequalities for smoothly embedded surfaces with \emph{negative} self-intersection number in smooth 4-manifolds of non-simple type. This will be achieved through a relation between the Seiberg-Witten invariants used to get adjunction inequalities of 4-manifolds of simple type and a blow-up formula.
Keywords : 4-manifolds, non-simple type, higher type adjunction inequalities, Seiberg-Witten invariants
MSC numbers : Primary 57R57, 57M40
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