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 . In the process, an explicit description of the mapping class group is given. We then apply this to give a counterexample to the simple loop conjecture for representations from the Klein bottle group to PGL(2, R).
Received: November 2, 2017
Daniel GomezDepartment of Mathematics
University of Pittsburgh