Relaxing Multicurves on the Twice Punctured Möbius Band

Abstract

Let N1,n (n ≥ 1) be a non-orientable surface of genus 1 with n punctures and one boundary component. Generalized Dynnikov coordinates provide a bijection between the set of multicurves in N1,n and Z2n−1 \ {0}. In this paper we restrict to the case where n = 2 and describe an algorithm to relax a multicurve in N1,2 making use of its generalized Dynnikov coordinates