Fibered links whose monodromy twists many times around a boundary component have large next-to-top link Floer homology, and braid closures with large fractional Dehn twist coefficient have large annular Khovanov homology.
The Birman-Hilden theory
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abstract
In the 1970s Joan Birman and Hugh Hilden wrote several papers on the problem of relating the mapping class group of a surface to that of a cover. We survey their work, give an overview of the subsequent developments, and discuss open questions and new directions.
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math.GT 1years
2026 1verdicts
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Fractional Dehn twist coefficients and rank bounds for categorified link invariants
Fibered links whose monodromy twists many times around a boundary component have large next-to-top link Floer homology, and braid closures with large fractional Dehn twist coefficient have large annular Khovanov homology.