We characterize the fractional Dehn twist coefficient of a braid in terms ofa slope of the homogenization of the Upsilon function, where Upsilon is thefunction-valued concordance homomorphism defined by Ozsv'ath, Stipsicz, andSzab'o. We use this characterization to prove that $n$-braids with fractionalDehn twist coefficient larger than $n-1$ realize the braid index of theirclosure. As a consequence, we are able to prove a conjecture of Malyutin andNetsvetaev stating that $n$-times twisted braids realize the braid index oftheir closure. We provide examples that address the optimality of our results.The paper ends with an appendix about the homogenization of knot concordancehomomorphisms.
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机译：我们以富硅函数的均质化斜率表示编织的分数Dehn扭转系数，其中upsilon是由ozsv 'Ath，Stipsicz，Andszab o定义的功能障碍的一致性均匀性。我们使用此表征来证明具有大于$ N-1 $大于$ N-1 $的FRACTIANYDEHN扭转系数的$ N $ -BRARF。因此，我们能够证明Malyutin Andnetsvetaev猜测指出，$ N $ -times扭曲的辫子实现了TheIr封闭的编织指标。我们提供了解决结果的最优性的例子。本文以关于结均质化的均质化的附录结束。
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