A Classification of Fundamental Group Elements Representing simple closed curves on the punctured Klein Bottle

2017/04/09 by Gomez, Daniel
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1704.02601

Abstract

In this paper we provide a classification of fundamental group elements representing simple closed curves on the punctured Klein bottle, Similar to the Birman-Series classification of curves on the punctured torus[1]. In the process, an explicit description of the mapping class group is given. We then apply this to give a counterexample the simple loop conjecture for representations from the Klein bottle group to PGL(2,R).

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