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Intermediate links of plane curves

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Abstract

For a smooth complex curve C ⊂ ℂ2 we consider the link Lr = C∂Br, where Br denotes an Euclidean ball of radius r > 0. We prove that the diagram Dr obtained from Lr by a complex stereographic projection satisfies χ(CBr) = rot(Dr)−wr(Dr). As a consequence we show that if Dr has no negative Seifert circles and Lr is strongly quasipositive and fibered, then the Yamada–Vogel algorithm applied to Dr yields a quasipositive braid.

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Correspondence to Arnaud Bodin.

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Bodin, A., Borodzik, M. Intermediate links of plane curves. Isr. J. Math. 227, 63–111 (2018). https://doi.org/10.1007/s11856-018-1716-y

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  • DOI: https://doi.org/10.1007/s11856-018-1716-y

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