A NOTE ON INDECOMPOSABLE 4-MANIFOLDS

Title & Authors
A NOTE ON INDECOMPOSABLE 4-MANIFOLDS
Cho, Yong-Seung; Hong, Yoon-Hi;

Abstract
In this note we show that there is an anti-symplectic involution $\small{\sigma\;:\;X\;\to\;X}$ on a simply-connected, closed, non-Kahler and symplectic 4-manifold X with a disjoint union of Riemann surfaces $\small{{\amalg}^n_{i=1}{\Sigma}_i,\;n\;{\ge}\;2}$ as a fixed point set. Also we show that its quotient X/$\small{\sigma}$ is homeomorphic to $\small{\mathbb{CP}^2{\sharp}r\mathbb{CP}^2}$ but not diffeomorphic to $\small{\mathbb{CP}^2{\sharp}r\mathbb{CP}^2,\;r\;=\;b_2^-(X/{\sigma})}$.
Keywords
non-Kahler symplectic 4-manifold;anti-symplectic involution;Dolgachev surface;Seiberg-Witten invariant;
Language
English
Cited by
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