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  1. ; ; (, Journal of the European Mathematical Society)
    For every integerg\ge 2we construct 3-dimensional genus-g1-handlebodies smoothly embedded inS^{4}with the same boundary, and which are defined by the same cut systems of their boundary, yet which are not isotopic rel. boundary via any locally flat isotopy even when their interiors are pushed intoB^{5}. This proves a conjecture of Budney–Gabai for genus at least 2. 
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