Stabilizations via Lefschetz fibrations and exact open books

Date

2017-01-01

Author

Arıkan, Mehmet Fırat

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We show that if a contact open book (Σ, h) on a (2n + 1)-manifold M (n ≥ 1) is induced by a Lefschetz fibration π : W → D2 , then there is a 1-1 correspondence between positive stabilizations of (Σ, h) and positive stabilizations of π. We also show that any exact open book, an open book induced by a compatible exact Lefschetz fibration, carries a contact structure. Moreover, we prove that there is a 1-1 correspondence (similar to the one above) between convex stabilizations of an exact open book and convex stabilizations of the corresponding compatible exact Lefschetz fibration. We also show that convex stabilization of compatible exact Lefschetz fibrations produces symplectomorphic completions.

Subject Keywords

Contact & symplectic structures, Open book, Lefschetz fibration, Stabilization

URI

https://hdl.handle.net/11511/71988
http://gokovagt.org/journal/2017/jggt17-akbuarik.pdf

Journal

Journal Gökova Geometry Topology

Collections

Department of Mathematics, Article

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Citation Formats

M. F. Arıkan, “Stabilizations via Lefschetz fibrations and exact open books,” Journal Gökova Geometry Topology, pp. 1–31, 2017, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/71988.