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http://dx.doi.org/10.4134/BKMS.2005.42.4.817

A NOTE ON INDECOMPOSABLE 4-MANIFOLDS  

Cho, Yong-Seung (DEPARTMENT OF MATHEMATICS, EWHA WOMEN'S UNIVERSITY)
Hong, Yoon-Hi (DEPARTMENT OF MATHEMATICS, EWHA WOMEN'S UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.42, no.4, 2005 , pp. 817-828 More about this Journal
Abstract
In this note we show that there is an anti-symplectic involution $\sigma\;:\;X\;\to\;X$ on a simply-connected, closed, non-Kahler and symplectic 4-manifold X with a disjoint union of Riemann surfaces ${\amalg}^n_{i=1}{\Sigma}_i,\;n\;{\ge}\;2$ as a fixed point set. Also we show that its quotient X/$\sigma$ is homeomorphic to $\mathbb{CP}^2{\sharp}r\mathbb{CP}^2$ but not diffeomorphic to $\mathbb{CP}^2{\sharp}r\mathbb{CP}^2,\;r\;=\;b_2^-(X/{\sigma})$.
Keywords
non-Kahler symplectic 4-manifold; anti-symplectic involution; Dolgachev surface; Seiberg-Witten invariant;
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