COMPATIBLE RELATIVE LEFSCHETZ FIBRATIONS ON ADMISSIBLE RELATIVE STEIN PAIRS

Date

2024-8

Author

Yıldırım, Yasemin

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For more than two decades it has been known that any compact Stein surface (of real dimension four) admits a compatible Lefschetz fibration over a two-disk. More recently, Giroux and Pardon have generalized this result by giving a complex geometric proof for the existence of compatible Lefschetz fibrations on Stein domains of any even dimension. As a preparatory step in proving the former, Akbulut and Ozbagci have shown that there exist infinitely many pairwise non-equivalent Lefschetz fibrations on the four-ball by using a result of Lyon constructing fibrations on the complements of (p,q)-torus links in the three- sphere. In this thesis, we first extend this result to obtain compatible Lefschetz fibrations on six-ball whose pages are (p, q, 2)-Brieskorn varieties, and then construct a compatible relative Lefschetz fibrations on any Stein domain (of dimension six) which admit a certain (admissible) relative Stein pair structure. In particular, we provide a purely topological proof for the existence of Lefschetz fibrations on specific 6-dimensional Stein domains.

Subject Keywords

Stein domain, Lefschetz Fibration, Contact Structure, Monodromy, Handle Decomposition

URI

https://hdl.handle.net/11511/110834

Collections

Graduate School of Natural and Applied Sciences, Thesis