Small genus-4 Lefschetz fibrations on simply-connected 4-manifolds

Altunöz, Tülin
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 CP2 #8 and CP2#9, 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.


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Altunöz, Tülin (2021-06-01)
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Analog of Grobman-Hartman theorem about stable and unstable manifolds solutions for differential equations in Banach spaces with degenerate Fredholm operator at the derivative are proved. In contrast to usual evolution equation here central manifold arises even in the case of spectrum absence on the imaginary axis. Jordan chains tools and implicit operator theorem are used. The obtained results allow to develop center manifold methods for computation of bifurcation solution asymptotics and their stability i...
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Citation Formats
T. Altunöz, “Small genus-4 Lefschetz fibrations on simply-connected 4-manifolds,” TURKISH JOURNAL OF MATHEMATICS, vol. 46, no. 4, pp. 1268–1290, 2022, Accessed: 00, 2022. [Online]. Available: