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The Birman-Hilden theory

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arxiv 1703.03448 v1 pith:5OOPWH36 submitted 2017-03-09 math.GT

Dan Margalit , Rebecca R. Winarski This is my paper · ORCID
classification math.GT
keywords birmanbirman-hildenclasscoverdevelopmentsdirectionsdiscussgive
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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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  1. Fractional Dehn twist coefficients and rank bounds for categorified link invariants

    math.GT 2026-08 conditional novelty 7.0 of 10

    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.

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