Browsing by Author "Altunoz, Tulin"

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    Generating the Mapping Class Group of a Nonorientable Surface by Two Elements or by Three Involutions
    (2022) Altunoz, Tulin; Pamuk, Mehmetcik; Yildiz, Oguz; https://orcid.org/0000-0002-9116-2253
    We prove that, for g >= 19 the mapping class group of a nonorientable surface of genus g, Mod(N-g), can be generated by two elements, one of which is of order g. We also prove that for g >= 26, Mod(N-g) can be generated by three involutions.
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    Small genus-4 Lefschetz fibrations on simply-connected 4-manifolds
    (2022) Altunoz, Tulin
    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<(CP2)over bar> and CP2#9<(CP2)over bar>, 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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    The Twıst Subgroup Is Generated By Two Elements
    (TOHOKU MATHEMATICAL JOURNAL, 2024-07-14) Altunoz, Tulin; Pamuk, Mehmetcik; Yildiz, Oguz
    We show that the twist subgroup T-g of a nonorientable surface of genus g can be generated by two elements for every odd g >= 21 and even g >= 50. Using these generators, we can also show that T-g can be generated by two or three commutators depending on g modulo 4. Moreover, we show that T-g can be generated by three elements if g >= 8. For this general case, the number of commutator generators is either three or four depending on g modulo 4 again.