Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3157
Abstract
We consider simply connected $4$-manifolds admitting Lefschetz fibrations over the $2$-sphere. We explicitly construct nonhyperelliptic and hyperelliptic Lefschetz fibrations of genus $4$ on simply-connected $4$-manifolds which are exotic symplectic $4$-manifolds in the homeomorphism classes of $\mathbb{C} P^{2}\#8\overline{\mathbb{C} P^{2}}$ and $\mathbb{C} P^{2}\#9\overline{\mathbb{C} P^{2}}$, respectively. From these, we provide upper bounds for the minimal number of singular fibers of such fibrations. In addition, we prove that this number is equal to $18$ for $g=3$ when such fibrations are hyperelliptic. Moreover, we discuss these numbers for higher genera.
Keywords
Symplectic $4$-manifolds, mapping class groups, Lefschetz fibrations, exotic manifolds
First Page
1268
Last Page
1290
Recommended Citation
ALTUNÖZ, TÜLİN
(2022)
"Small genus-$4$ Lefschetz fibrations on simply-connected $4$-manifolds,"
Turkish Journal of Mathematics: Vol. 46:
No.
4, Article 10.
https://doi.org/10.55730/1300-0098.3157
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss4/10
