Let (E, M, P) be a surface with marked points M c_ JE & iquest; and punctures P c_ E \ JE. We show that for every curve y on E \ P, the curve obtained by resolving the kinks of y in any order is uniquely determined, up to homotopy in E \ P, by the 2-orbifold homotopy class of y, in which the punctures are interpreted to be orbifold points of order 2. Our proof relies on an application of the diamond lemma.
On the resolution of kinks of curves on punctured surfaces
Labardini Fragoso D.
2025
Abstract
Let (E, M, P) be a surface with marked points M c_ JE & iquest; and punctures P c_ E \ JE. We show that for every curve y on E \ P, the curve obtained by resolving the kinks of y in any order is uniquely determined, up to homotopy in E \ P, by the 2-orbifold homotopy class of y, in which the punctures are interpreted to be orbifold points of order 2. Our proof relies on an application of the diamond lemma.
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