Low-slope Lefschetz fibrations

Çengel, Adalet
Korkmaz, Mustafa
For any g ≥ 3, we construct genus-g Lefschetz fibrations over the two-sphere whose slopes are arbitrarily close to 2. The total spaces of the Lefschetz fibrations can be chosen to be minimal and simply connected. It is also shown that the infimum and the supremum of slopes of all Lefschetz fibrations over the two-sphere are not realized as slopes.
Journal of Topology and Analysis


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For an integer m ≥ 2let ξm denote a primitive complex m − th root of unity. We call a v-periodic sequence a = (a1, a1, ..., av−1, ...) an m − ary sequence if a1, a1, ..., av−1 ∈ εm. (εm = 1, ξm, ξ2 m, ξ(m−1) m ). An almost m-ary sequence if a0 = 0anda0, a1, ..., av−1 ∈ εm.. For 1 ≤ t ≤ v1 the autocorrelation function Ca(t) is defined by Ca(t) = vX−1 i=0 aiai+t where a is the complex conjugate of a. An m − ary or almost m − ary sequence a of period v is called a perfect sequence (PS) if Ca(t) = 0 for all 1 ≤...
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Citation Formats
A. Çengel and M. Korkmaz, “Low-slope Lefschetz fibrations,” Journal of Topology and Analysis, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85108193873&origin=inward.