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THE SLICE-BENNEQUIN INEQUALITY FOR THE FRACTIONAL DEHN TWIST COEFFICIENT
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- Journal:
- Journal of the Institute of Mathematics of Jussieu , First View
- Published online by Cambridge University Press:
- 20 September 2024, pp. 1-17
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- Article
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We characterize the fractional Dehn twist coefficient (FDTC) on the n-stranded braid group as the unique homogeneous quasimorphism to
$\mathbb {R}$ of defect at most 1 that equals 1 on the positive full twist and vanishes on the 
$(n-1)$-stranded braid subgroup. In a different direction, we establish that the slice-Bennequin inequality holds with the FDTC in place of the writhe. In other words, we establish an affine linear lower bound for the smooth slice genus of the closure of a braid in terms of the braid’s FDTC. We also discuss connections between these two seemingly unrelated results. In the appendix, we provide a unifying framework for the slice-Bennequin inequality and its counterpart for the FDTC.
