Simplified broken Lefschetz fibrations and trisections of 4-manifolds

Abstract

Shapes of four dimensional spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, in order to derive simple decompositions into much better understood manifold pieces. Our methods not only allow us to produce various interesting families of examples, but also to establish a correspondence between simplified broken Lefschetz fibrations and simplified trisections of closed, oriented 4-manifolds.

17 pages, 7 figures

References in corpus (3)

• Genus two trisections are standard
• Simplifying indefinite fibrations on 4-manifolds
• Broken Lefschetz fibrations and smooth structures on 4-manifolds

Cited by in corpus (4)

• Trisections of 3-manifold bundles over $S^1$
• Symplectic 4-manifolds admit Weinstein trisections
• Embeddings of $4$--manifolds in $\CP^3$
• Vertical 3-manifolds in simplified (2, 0)-trisections of 4-manifolds