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- W1559972068 abstract "A classical inequality which is due to Lickorish and Hempel says that the distance between two curves in the curve complex can be measured by their intersection number. In this paper, we show a converse version; the intersection number of two curves can be measured by the sum of all subsurface projection distances between them. As an application of this result, we obtain a coarse decreasing property of the intersection numbers of the multicurves contained in tight multigeodesics. Furthermore, by using this property, we give an algorithm for determining the distance between two curves in the curve complex. Indeed, such algorithms have also been found by Birman–Margalit–Menasco, Leasure, Shackleton, and Webb: we will briefly compare our algorithm with some of their algorithms, for detailed quantitative comparison of all known algorithms including our algorithm, we refer the reader to the paper of Birman–Margalit–Menasco [1]." @default.
- W1559972068 created "2016-06-24" @default.
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- W1559972068 date "2016-06-14" @default.
- W1559972068 modified "2023-10-14" @default.
- W1559972068 title "Intersection numbers in the curve complex via subsurface projections" @default.
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- W1559972068 doi "https://doi.org/10.1142/s1793525317500169" @default.
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