A note on embedding of achiral Lefschetz fibrations
Arijit Nath, Kuldeep Saha

TL;DR
This paper explores embeddings of achiral Lefschetz fibrations in higher-dimensional manifolds, providing new proofs and conditions for embedding in specific 6-dimensional spaces, with implications for 4-manifold theory.
Contribution
It offers a new proof that all closed orientable 4-manifolds embed in S^2×S^2×S^2 and characterizes conditions for embedding achiral Lefschetz fibrations with hyperelliptic monodromy in D^6.
Findings
Every closed orientable 4-manifold embeds in S^2×S^2×S^2.
Achiral Lefschetz fibrations with hyperelliptic monodromy embed in D^6.
An obstruction to LF embeddings is discussed.
Abstract
We discuss -dimensional achiral Lefschetz fibrations bounding -dimensional open books and study their Lefschetz fibration (LF) embedding in a bounded -dimensional manifold, in the sense of Ghanwat--Pancholi. As an application we give another proof of the fact that every closed orientable -manifold embeds in . We also show that every achiral Lefschetz fibration with hyperelliptic monodromy admits LF embedding in and discuss an obstruction to such LF embeddings.
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.
Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Geometry and complex manifolds
