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Author ORCID Identifier
Open Access Dissertation
Doctor of Philosophy (PhD)
Year Degree Awarded
Month Degree Awarded
Geometry and Topology
In this thesis we seek to better understand the planar mapping class group in
order to find factorizations of boundary multitwists, primarily to generate and study
symplectic Lefschetz pencils by lifting these factorizations. Traditionally this method
is applied to a disk or sphere with marked points, utilizing factorizations in the stan-
dard and spherical braid groups, whereas in our work we allow for multiple boundary components. Dehn twists along these boundaries give rise to exceptional sections of Lefschetz fibrations over the 2–sphere, equivalently, to Lefschetz pencils with base points. These methods are able to derive an array of known examples of Lefshetz fibrations while giving their maximal exceptional sections. In particular, a family of examples we obtain, which recapture unpublished examples by Baykur, Hamada and Korkmaz, allows us to demonstrate that two well-known inequalities on the number of non-separating and separating vanishing cycles are in fact sharp for every genus g ≥ 2.
Buckman, Richard E., "POSITIVE FACTORIZATIONS VIA PLANAR MAPPING CLASSES AND BRAIDS" (2023). Doctoral Dissertations. 2961.
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