Band surgeries and crossing changes between fibered links

Abstract

We characterize cutting arcs on fiber surfaces that produce new fiber surfaces, and the changes in monodromy resulting from such cuts. As a corollary, we characterize band surgeries between fibered links and introduce an operation called Generalized Hopf banding. We further characterize generalized crossing changes between fibered links, and the resulting changes in monodromy.

27 pages, 10 figures. New version has substantially shortened proof of a key lemma. Additionally, results about monodromy changes have been added

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• Right-veering diffeomorphisms of compact surfaces with boundary II
• On the stable equivalence of open books in three-manifolds
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Cited by in corpus (2)

• Distance one lens space fillings and band surgery on the trefoil knot
• Cosmetic two-strand twists on fibered knots