Non-complex symplectic 4-manifolds with $b_{2}^{+}=1$

Details Non-complex symplectic 4-manifolds with $b_{2}^{+}=1$ Non-complex symplectic 4-manifolds with $b_{2}^{+}=1$

2001-08-31

arxiv.org/abs/math/0108220v1

Mathematics

Geometric Topology

AMS-LaTeX file, 7 pages

Scientific paper

In this short article we give a criterion whether a given minimal symplectic 4-manifold with $b_{2}^{+}=1$ having a torsion-free canonical class is rational or ruled. As a corollary, we confirm that most of homotopy elliptic surfaces $E(1}_{K}$, K is a fibered knot in $S^3$, constructed by R. Fintushel and R. Stern are minimal symplectic 4-manifolds with $b_{2}^{+}=1$ which do not admit a complex structure.

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