TL;DR
This paper explores open book foliations in 3-manifolds, providing new formulas and proofs that connect contact geometry, braid theory, and mapping class groups, advancing understanding in low-dimensional topology.
Contribution
It introduces a braid-theoretic formula for the self-linking number and offers a combinatorial proof of the Bennequin-Eliashberg inequality, linking contact geometry with mapping class group theory.
Findings
Derived a braid-theoretic formula for self-linking number
Established a connection to Johnson-Morita homomorphism
Provided an alternative proof of the Bennequin-Eliashberg inequality
Abstract
We study open book foliations on surfaces in 3-manifolds, and give applications to contact geometry of dimension 3. We prove a braid-theoretic formula of the self-linking number of transverse links, which reveals an unexpected link to the Johnson-Morita homomorphism in mapping class group theory. We also give an alternative combinatorial proof to the Bennequin-Eliashberg inequality.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.