Off-campus UMass Amherst users: To download campus access dissertations, please use the following link to log into our proxy server with your UMass Amherst user name and password.

Non-UMass Amherst users: Please talk to your librarian about requesting this dissertation through interlibrary loan.

Dissertations that have an embargo placed on them will not be available to anyone until the embargo expires.

Author ORCID Identifier


Open Access Dissertation

Document Type


Degree Name

Doctor of Philosophy (PhD)

Degree Program


Year Degree Awarded


Month Degree Awarded


First Advisor

Inanc Baykur

Subject Categories

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 In particular, a family of examples we obtain, which recapture unpublished examples by Baykur, Hamada and Korkmaz, allows us to demonstrate that two well-known inequalities on the number of non-separating and separating vanishing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.


Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License