Intersections of Multicurves on Small Genus Non–Orientable Surfaces
Intersections of Multicurves on Small Genus Non–Orientable Surfaces
Let $K_{n}$ ($n>1$) be an $n$--punctured non--orientable surface of genus $2$ with 1 boundary component. We give formulae for calculating the geometric intersection number of an arbitrary multicurve with a relaxed multicurve on $K_{n}$ given their generalized Dynnikov coordinates.
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- [1] T. Hall, S. O¨ . Yurttas¸, Intersections of multicurves from Dynnikov coordinates, Bull. Aust. Math. Soc, 98, (2018), 149-158.
- [2] S. O¨ . Yurttas¸, Geometric intersection of curves on punctured disks, J. Math. Soc. Japan, 65(4) (2013), 1153-1168.
- [3] I. Dynnikov, On a Yang-Baxter mapping and the Dehornoy ordering, Uspekhi Mat. Nauk, 57(345) (2002), 151-152.
- [4] A. Papadopoulos, R.C. Penner, Hyperbolic metrics, measured foliations and pants decompositions for non-orientable surfaces, Asian J. Math, 20
(2016), 157-182.
- [5] M. Pamuk, S. O¨ . Yurttas¸, Integral laminations on non–orientable surfaces, Turkish J. Math, 42 (2018), 69-82.