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Small genus-4 Lefschetz fibrations on simply-connected 4-manifolds
Date
2022-03-07
Author
Altunöz, Tülin
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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.
Subject Keywords
Symplectic 4-manifolds
,
mapping class groups
,
Lefschetz fibrations
,
exotic manifolds
,
SINGULAR FIBERS
,
MINIMAL NUMBER
,
SMOOTH STRUCTURES
,
SIGNATURE
URI
https://hdl.handle.net/11511/98994
Journal
TURKISH JOURNAL OF MATHEMATICS
DOI
https://doi.org/10.3906/mat-2108-85
Collections
Department of Mathematics, Article
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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: https://hdl.handle.net/11511/98994.