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Genus two Lefschetz fibrations with b+2=...
Akhmedov, Anar...

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Genus two Lefschetz fibrations with b+2=1 and c12=1,2 by Akhmedov, Anar ( Author )
Lemonjar Open Access
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06-09-2015
In this article we construct a family of genus two Lefschetz fibrations fn:Xθn→S2 with e(Xθn)=11, b+2(Xθn)=1, and c21(Xθn)=1 by applying a single lantern substitution to the twisted fiber sums of Matsumoto's genus two Lefschetz fibration over S2. Moreover, we compute the fundamental group of Xθn and show that it is isomorphic to the trivial group if n=−3 or −1, Z if n=−2, and Z|n+2| for all integers n≠−3,−2,−1. Also, we prove that our fibrations admit −2 section, show that their total space are symplectically minimal, and have the symplectic Kodaira dimension κ=2. In addition, using the techniques developed in \cite{A, AP1, ABP, AP2, AZ, AO}, we also construct the genus two Lefschetz fibrations over S2 with c21=1,2 and χ=1 via the fiber sums of Matsumoto's and Xiao's genus two Lefschetz fibrations, and present some applications in constructing exotic smooth structures on small 4-manifolds with b+2=1 and b+2=3.
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Article
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English
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MYR 0.00
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https://arxiv.org/abs/1509.01853
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