Lefschetz fibrations over the disc

Abstract

We provide a complete set of moves relating any two Lefschetz fibrations over the disk having as their total space the same 4-dimensional 2-handlebody up to 2-equivalence. As a consequence, we also obtain moves relating diffeomorphic 3-dimensional open books, providing a different approach to an analogous previous result by Harer.

Improved exposition, now equivalent to the published one; 51 pages, 67 figures

References in corpus (5)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• On the stable equivalence of open books in three-manifolds
• Covering moves and Kirby calculus
• A universal ribbon surface in B^4
• A universal invariant of four-dimensional 2-handlebodies and three-manifolds

Cited by in corpus (5)

• A diagrammatic presentation and its characterization of non-split compact surfaces in the 3-sphere
• On embeddings of almost complex manifolds in almost complex Euclidean spaces
• Braiding link cobordisms and non-ribbon surfaces
• Compact Stein surfaces as branched covers with same branch sets
• Universal Lefschetz fibrations and Lefschetz cobordisms