An algebraic characterization of a Dehn twist for nonorientable surfaces

2015/01/28 by Atalan, Ferihe
#20F38 #57N05 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1501.07183

Abstract

Let N_g^k be a nonorientable surface of genus g≥ 5 with k-punctures. In this note, we will give an algebraic characterization of a Dehn twist about a simple closed curve on N_g^k. Along the way, we will fill some little gaps in the proofs of some theorems in \citeA and \citeI1 giving algebraic characterizations of Dehn twists about separating simple closed curves. Indeed, our results will give an algebraic characterization for the topological type of Dehn twists about separating simple closed curves.

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